/H 1 /H 1 Ce corrigé sera rendu public le 1er octobre 2021. [(x)4.88446]TJ [(1)-6.01515(4)-499.86(A)27.1167(t)3.3531(t)3.3531(e)-1.33286(n)25.4383(t)3.3531(i)0.671944(o)-6.01515(n)-323.867(à)-343.275(n)1.3483(e)-326.549(p)1.3483(a)-6.01515(s)-328.353(a)-6.01515(p)1.3483(p)-22.7417(e)-1.3336(l)0.671944(e)-1.3336(r)-331.13(l)0.671944(a)-331.23(f)4.35514(o)-6.01515(n)1.3483(c)-1.3336(t)3.35237(i)0.671944(o)-6.01515(n)1.3483]TJ q 4 0 0 -100 767.9 3839.9 cm -256.56 -12 Td 0 0 1 rg )0.671944]TJ 202.08 0 Td ET Bonne préparation à tous. Dans ce domaine, les nombres premiers servent de base au principe de clés publique et privée qui permettent, au travers d’algorithmes, d’échanger des messages chiffrés. /R21 9.96264 Tf LOGICIEL INFORMATIQUE COMMERCIAL – BREVET Mention relative aux droits restreints du gouvernement des États-Unis. 9.96 0 Td [(L)-1.49607(a)-331.23(d)1.3483(e)-1.33286(r)-5.91443(n)1.3483(i)0.671944(è)-1.3336(r)-5.91517(e)-326.549(p)1.3483(a)-6.01515(r)-5.91517(t)3.35237(i)0.671944(e)-1.3336(,)-324.543(t)3.35237(r)-5.91517(è)-1.3336(s)-328.353(c)-1.3336(o)-6.01515(u)1.3483(r)-5.91517(t)3.35237(e)-1.3336(,)-324.543(p)-22.7417(o)-6.01515(r)-5.91517(t)3.35237(e)-326.547(s)-3.1377(u)1.34683(r)-331.129(l)0.673414(e)-1.33213(s)-328.353(b)1.34683(a)-6.01368(s)-3.1377(e)-1.33213(s)-328.353(d)1.34683(e)-338.592(d)1.34683(o)-6.01368(n)1.34683(n)1.34683(é)]TJ 72.84 0 Td /BPC 1 8.33333 0 0 8.33333 0 0 cm BT Q /BPC 1 [(e)-1.33286(s)-3.1377(t)-333.908(l)0.671944(')0.671944(o)-6.01515(p)-22.7417(é)-1.3336(r)-5.91517(a)-6.01515(t)3.35237(e)-1.3336(u)1.3483(r)-319.085(a)-6.01515(s)-3.1377(s)-3.1377(o)-30.1051(c)-1.3336(i)0.671944(é)-326.549(à)-331.23(l)0.671944(a)-331.23(d)1.3483(i)0.671944(v)-2.33195(i)0.673414(s)-3.1377(i)0.673414(o)-6.01368(n)-323.868()1.34683(o)-6.01368(t)3.35237(t)3.35237(a)-6.01368(n)25.4368(t)3.35237(e)-326.547(e)-1.33213(n)-335.913(P)5.86664(y)-2.33195(t)3.35237(h)1.34683(o)-6.01368(n)1.34683(. ID /BPC 1 T*[(r)-5.10869(t)-5.10869(o)-5.10869(l)-510.999(=)-523.044(1)-5.10942(e)-5.10942(-)-5.10942(8)-5.10942]TJ 40 0 obj ET /R19 9.96264 Tf )-5.10795(5)-5.10942(\))-5.10942(\))-5.10942]TJ [(. 0 0 0 1 k Le rapport entier pour 2019 et ceux des années précédentes sont disponibles sur le site du concours. 8.33333 0 0 8.33333 0 0 cm BT /R19 9.96264 Tf [(a)-5.10869(t)-5.10869(o)-5.10869(l)-510.999(=)-523.044(1)-5.10942(e)-5.10942(-)-5.10942(5)-5.10942]TJ 1 0 0 1 160.56 18.48 Tm /R17 9.96264 Tf [(q)-2.33122(u)1.3483(i)-324.543(e)-1.33286(s)-3.1377(t)-333.907(r)-5.91443(é)-1.33286(p)-22.7417(é)-1.33286(t)3.3531(é)-326.549(q)-2.33195(u)1.3483(a)-6.01515(t)3.35237(r)-5.91517(e)-326.549(f)4.35514(o)-6.01515(i)0.671944(s)-3.1377(. [(2)-3.30091]TJ q /R29 9.96264 Tf -15 -15.48 Td q 6 0 Td )0.673414]TJ Q stream 6 0 Td /R9 gs 1 0 0 1 218.76 674.04 Tm [(T)6.05452(é)1.64678(l)4.40938(é)1.64678(c)1.64188(h)-4.59889(a)25.2865(r)3.0338(g)5.19519(é)-359.703(g)5.19519(r)3.0338(a)-1.48014(t)-3.68238(u)-4.59889(i)4.40938(t)-3.68238(e)1.64678(m)-0.227085(e)1.64678(n)-4.60052(t)-338.266(s)5.76699(u)-4.60052(r)3.03216]TJ /R34 8.96638 Tf /R21 9.96264 Tf [(n)1.3483(o)-6.01515(m)2.02392(s)-340.398(g)-6.01515(l)0.671944(o)-6.01515(b)1.3483(a)-6.01515(l)-312.498(d)1.3483(u)-335.912(p)1.3483(r)-5.91517(o)-6.01515(g)-6.01515(r)-5.91517(a)-6.01515(m)2.02465(m)2.02465(e)-169.964(:)0.671944]TJ 8.33333 0 0 8.33333 0 0 cm BT [(à)-415.544(u)1.34683(n)1.34683(e)-410.862(s)-3.1377(é)-1.33213(r)-5.91369(i)0.673414(e)-398.817(q)-2.33195(u)1.34683(e)-1.33213]TJ /IM true 17.64 0 Td Base de données des concours. 266.4 0 Td See more of Concours mines ponts MP PC PSI PT Sujet et corrigé on Facebook. [(/)-5.10869]TJ 1 0 0 1 80.76 622.68 Tm /R29 9.96264 Tf 1 0 0 1 98.4 438.84 Tm [(2)-6.01515(2)-499.86(O)-5.33879(b)1.3483(s)-3.1377(e)-1.33286(r)-5.91443(v)21.7588(e)-1.33286(r)-319.084(q)-2.33122(u)1.3483(e)-350.639(s)-3.1377(u)1.3483()2.02465(s)-3.1377(a)-6.01515(m)2.02465(m)2.02465(e)-1.3336(n)25.4383(t)-333.908(p)1.3483(r)-5.91517(o)-30.1051(c)22.7564(h)1.3483(e)-338.594(d)1.3483(e)-350.639(1)-6.01515(,)-348.633(l)0.673414(e)-1.33213(s)-340.398(r)-5.91369(e)-1.33213(c)-1.33213(t)3.35237(a)-6.01368(n)1.34683(g)-6.01368(l)0.673414(e)-1.33213(s)-328.353(à)-355.319(g)-6.01368(a)-6.01368(u)1.34683(c)]TJ )-300.452(I)-0.329355(l)-312.497(e)-1.33213(s)-3.1377(t)-297.773(r)-5.91369(e)-1.33213(l)0.673414(a)-6.01368(t)3.35237(i)0.673414(v)21.758(e)-1.33213(m)2.02318(e)]TJ /R19 9.96264 Tf [(x)4.88446]TJ [(1)-6.01515(9)-499.86(Q)-5.33879(u)1.3483(e)-1.33286(s)-3.1377(t)3.3531(i)0.671944(o)-6.01515(n)-323.867(d)1.3483(e)-350.638(c)-1.3336(o)-6.01515(u)1.3483(r)-5.91517(s)-3.1377(. 8.33333 0 0 8.33333 0 0 cm BT BI [(=)-5.89017]TJ /R14 7.97011 Tf -276.12 -12 Td /H 1 [(C)-0.657241(e)-374.728(s)-3.1377(u)1.3483(j)4.35514(e)-1.33286(t)-382.087(a)-6.01515(b)-22.7417(o)-6.01515(r)-5.91517(d)1.3483(e)-362.684(p)1.3483(l)0.671944(u)1.3483(s)-3.1377(i)0.671944(e)-1.3336(u)1.3483(r)-5.91517(s)-364.488(p)1.3483(r)-5.91517(o)-6.01515(b)1.3483(l)0.671944(è)-1.3336(m)2.02465(e)-1.3336(s)-376.533(n)25.4368(u)1.34683(m)2.02318(é)-1.33213(r)-5.91369(i)0.673414(q)-2.33195(u)1.34683(e)-1.33213(s)-364.488(l)0.673414(i)0.673414(é)-1.33213(s)-376.533(a)-6.01368(u)1.34683(x)-363.682(n)1.34683(o)-6.01368(m)]TJ BI [(e)-1.33286(n)-408.182(1)-6.01515(. ET [(r)-5.91369(. /IM true q /R21 9.96264 Tf /R19 9.96264 Tf Les sujets sont fournis sans corrigés. BI 1 0 0 1 98.4 450.84 Tm /R19 9.96264 Tf /W 1 Ils sont accompagnés d'éléments de correction proposés par des enseignants de CPGE membres de l'UPSTI. 0 0 0 1 k 9.96 0 Td 8.33333 0 0 8.33333 0 0 cm BT 260.4 0 Td Q -58.08 -12 Td Ses rédacteurs, correcteurs, ont formulé des conseils pratiques. q [(q)-2.33122(u)1.3483(e)-1.33286(s)-3.1377(t)3.3531(i)0.671944(o)-6.01515(n)-323.867(5)-6.01515(. [(s)-3.1377(a)-331.23(v)57.8938(a)-6.01515(l)0.671944(e)-1.33286(u)1.3483(r)-174.544(:)0.671944]TJ 0 0 0 1 k /IM true Mines-Ponts 2019 Informatique Commun Epreuve, Concours Commun Mines Ponts (CCMP), Concours Informatique MP, AlloSchool Mines 2019. [(. [(c)-1.33213(e)-362.682(d)1.34683(e)-1.33213(s)-376.533(f)4.35514(o)-6.01368(n)1.34683(c)-1.33213(t)3.35237(i)0.673414(o)-6.01368(n)1.34683(s)-3.1377]TJ [(d)1.3483(e)-362.683(m)2.02392(é)-1.33286(m)2.02465(o)-6.01515(i)0.671944(r)-5.91517(e)-1.3336(. 1 0 0 1 272.16 18.48 Tm Mines Informatique MP-PC-PSI 2019 — Corrigé Ce corrigéest proposé par Virgile Andreani (ENS Ulm); il a été relu par Benjamin Monmege (enseignant-chercheur à l’université) et Guillaume Batog (professeur en CPGE). [(1)-6.01368(3)-6.01368]TJ [(\()3.35237(o)-6.01515(u)1.3483]TJ Mines Informatique MP-PC-PSI 2019 -- Corrigé Ce corrigé est proposé par Virgile Andreani (ENS Ulm) ; il a été relu par Benjamin Monmege (enseignant-chercheur à l'université) et Guillaume Batog (professeur en CPGE). /R21 9.96264 Tf 2019-1-Corrigé-Vidéo. [(s)-3.1377(e)-302.457(d)1.34683(e)-314.502(l)0.673414(a)-307.139(s)-3.1377(i)0.673414(n)1.34683(g)-6.01368(u)1.34683(l)0.673414(a)-6.01368(r)-5.91369(i)0.673414(t)3.35237(é)-1.33213]TJ q BI 8.33333 0 0 8.33333 0 0 cm BT ID Log In. 35.16 0 Td q 184.08 0 Td [(L)-1.49607(a)-319.185(p)1.3483(r)-5.91443(e)-1.33286(m)2.02465(i)0.671944(è)-1.3336(r)-5.91517(e)-302.459(p)1.3483(a)-6.01515(r)-5.91517(t)3.35237(i)0.671944(e)-302.459(e)-1.3336(s)-3.1377(t)-309.818(p)-22.7417(e)-1.3336(u)-323.867(l)0.671944(i)0.671944(é)-1.3336(e)-302.459(a)-6.01515(u)-311.822(r)-5.91517(e)-1.33213(s)-3.1377(t)3.35237(e)-314.502(e)-1.33213(t)-309.818(d)1.34683(e)-1.33213(m)2.02318(a)-6.01368(n)1.34683(d)1.34683(e)-314.502(l)0.673414(')0.673414(é)-1.33213(c)-1.33213(r)-5.91369(i)0.673414(t)3.35237(u)1.34683(r)]TJ /IM true Mines 2019. ID Information concernant les épreuves d’admissibilité À partir du prochain concours 2021, les épreuves écrites de la Banque Mines-Ponts (CCMP, CMT et TPE-EIVP) se dérouleront sur 4 journées consécutives.. Ainsi, cette année, les épreuves écrites auront lieu … ET /H 1 )4.3718]TJ 8.33333 0 0 8.33333 0 0 cm BT q Q Q [(2)-6.01515(4)-499.86(A)27.1167(t)3.3531(t)3.3531(e)-1.33286(n)25.4383(t)3.3531(i)0.671944(o)-6.01515(n)-396.137(à)-403.5(l)0.671944(a)-403.5(c)-1.3336(o)-6.01515(n)1.3483(f)4.35514(u)1.3483(s)-3.1377(i)0.671944(o)-6.01515(n)-396.137(e)-1.3336(n)25.4383(t)3.35237(r)-5.91517(e)-1.3336]TJ [(\r)-3.51656]TJ q 105 0 0 -4 530.9 3358.9 cm q 0.12 0 0 0.12 0 0 cm (li)Tj 8.33333 0 0 8.33333 0 0 cm BT 261.48 0 Td Dans ce domaine, les nombres premiers servent de base au principe de clés publique et privée qui permettent, au travers d’algorithmes, d’échanger des messages chiffrés. 94.2 0 Td EI Q [(\r)-3.51656]TJ [(q)-2.33195(u)1.34683(i)-348.632(s)-3.1377(')0.673414(a)-6.01368(p)1.34683(p)1.34683(u)1.34683(i)0.673414(e)-1.33213]TJ [(3)-499.86(R)1.18436(a)-6.01515(p)1.3483(p)-22.7417(e)-1.33286(l)-167.958(:)0.671944]TJ /W 1 Et aussi une correction de l’epreuve 0 disponible sur le site de mines-ponts [(A)20.448(n)-4.03313(n)-4.03313(a)5.09472(l)2.54662(e)2.1761(s)-362.094(d)5.09325(e)2.1761(s)-362.094(C)4.72272(o)5.09325(n)-4.03166(c)50.3561(o)5.09325(u)-5.49024(rs)-0.74399]TJ [(é)-1.33213(. <> /R29 9.96264 Tf /W 1 8.88 0 Td ID [(n)1.3483(o)-6.01515(m)2.02392(s)-424.713(g)-6.01515(l)0.671944(o)-6.01515(b)1.3483(a)-6.01515(l)-408.858(a)18.0749(v)21.758(e)-1.3336(c)-1.3336]TJ -2.52 -0.24 Td /R19 9.96264 Tf )0.673414]TJ %Çì¢ 259.08 0 Td 8.33333 0 0 8.33333 0 0 cm BT [(p)1.3483(u)-432.272(i)0.671944(m)2.02465(p)-22.7417(o)-6.01515(r)-5.91517(t)3.35237(e)-1.3336(r)-427.49(t)3.35237(o)-6.01515(u)1.3483(t)-430.268(l)0.671944(e)-434.954(m)2.02465(o)-30.1051(d)1.3483(u)1.3483(l)0.671944(e)-434.954(d)1.3483(')0.671944(u)1.3483(n)-444.317(c)-1.33213(o)-6.01368(u)1.34683(p)1.34683(,)-420.902(e)-1.33213(n)-444.318(f)4.35514(a)-6.01368(i)0.673414(s)-3.1377(a)-6.01368(n)25.4368(t)-418.223(a)-6.01368(t)3.35237(t)3.35237(e)-1.33213(n)25.4368(t)3.35237(i)0.673414(o)-6.01368(n)-420.228(p)1.34683(a)]TJ 8.33333 0 0 8.33333 0 0 cm BT q [(q)-2.33195(u)1.34683(e)-1.33213(m)2.02318(e)-1.33213(n)25.4368(t)-297.773(d)1.34683(a)-6.01368(n)1.34683(s)-304.263(l)0.673414(')0.673414(e)-1.33213(s)-3.1377(p)1.34683(a)-6.01368(c)-1.33213(e)-290.412(d)1.34683(e)-1.33213]TJ [(p)1.34683(a)-6.01368(r)-5.91369]TJ ID /W 1 [(q)-2.33122(u)1.3483(e)-362.683(d)1.3483(e)-362.683(q)-2.33122(u)1.3483(e)-1.33286(l)0.671944(q)-2.33122(u)1.3483(e)-1.3336(s)-352.443(f)4.35514(o)-6.01515(n)1.3483(c)-1.3336(t)3.35237(i)0.671944(o)-6.01515(n)1.3483(s)-352.443(d)1.3483(u)-347.957(m)2.02465(o)-30.1051(d)1.3483(u)1.3483(l)0.671944(e)-1.3336(,)-360.678(e)-1.3336(t)-357.998(q)-2.33195(u)1.34683(')0.673414(i)0.673414(l)-360.677(n)1.34683(')0.673414(y)-351.637(a)-355.319(p)1.34683(a)-6.01368(s)-352.443(d)1.34683(e)-362.682(r)-5.91369(i)0.673414(s)-3.1377(q)]TJ 29.52 0 Td [(n)25.4368(t)-297.773(c)-1.33213(o)-6.01368(m)2.02318(p)1.34683(l)0.673414(e)-1.33213(t)3.35237(,)-312.497(b)1.34683(i)0.673414(e)-1.33213(n)-311.823(p)-22.7432(o)-6.01368(s)-3.1377(é)-1.33213(,)-312.497(e)-1.33213(t)3.35237]TJ q 4 0 0 -100 767.9 4345.9 cm Copyright © 2021 UPSTI. Les modèles mathématiques ont permis de comprendre pourquoi il a été possible d'éradi-quer la variole à la fin des années 1970 et pourquoi il est plus difficile d'éradiquer d'autres maladies comme la poliomyélite ou la rougeole. Q <> )4.3718]TJ [(c)1.64269]TJ ET ID -9.96 -15.48 Td Q T*[(d)-5.10869(e)-5.10869(f)-523.044(s)-5.10869(o)-5.10869(n)-5.10869(t)-5.10869(_)-5.10869(p)-5.10795(r)-5.10869(o)-5.10942(c)-5.10942(h)-5.10942(e)-5.10942(s)-5.10795(\()-5.10942(x)-5.10942(,)-450.776(y)-5.10942(\))-5.10942(:)-5.10942]TJ q )0.673414]TJ 270.36 0 Td q 0 0 0 1 k Tous droits réservés. ET [(m)2.02318(-)-4.01108]TJ S.V.P. /BPC 1 -15 -15.36 Td [(1)-6.01368(3)-6.01368]TJ q 709 0 0 -9 1700.9 4650.9 cm /W 1 8.33333 0 0 8.33333 0 0 cm BT /R19 9.96264 Tf /R48 9.96264 Tf 9.6 0 Td 236.88 0 Td /R19 9.96264 Tf 1 0 0 1 54.96 674.28 Tm Q 8.33333 0 0 8.33333 0 0 cm BT stream /BPC 1 q /IM true [(&)-1.90592]TJ q q 4 0 0 -179 767.9 4246.9 cm [(n)1.34683(o)-6.01368(m)26.1132(b)1.34683(r)-5.91369(e)-1.33213(s)-292.218(p)1.34683(r)-5.91369(e)-1.33213(m)2.02318(i)0.673414(e)-1.33213(r)-5.91369(s)-3.1377(,)0.673414]TJ Corrigé UPSTI : Ce corrigé sera rendu public le 1er octobre 2021 . q 105 0 0 -4 530.9 5271.9 cm 8.33333 0 0 8.33333 0 0 cm BT 1 0 0 1 98.4 426.96 Tm 282.72 0 Td -276.84 -12 Td BI [()3.88463]TJ /BPC 1 Q /W 1 [(1)-3.30091]TJ [(r)-439.534(l)0.673414(a)-427.589(s)-3.1377(u)1.34683(i)0.673414(t)3.35237(e)-434.952(à)-6.01368]TJ /H 1 q 3048 0 0 -4 436.9 5587.9 cm [(b)1.34683(r)-5.91369(e)-1.33213(s)-364.488(p)1.34683(r)-5.91369(e)-1.33213(m)2.02318(i)0.673414(e)-1.33213(r)-5.91369(s)-3.1377(,)-360.677(n)1.34683(o)-6.01368(-)-4.01108]TJ -2.64 -0.24 Td 1 0 0 1 419.64 674.04 Tm EI Q [(i)0.673414(m)2.02318(a)-6.01368(l)0.673414(i)0.673414(t)3.35237(é)-326.547(d)1.34683(e)-338.592(F)86.5029(e)-1.33213(r)-5.91369(m)2.02318(a)-6.01368(t)3.35237(,)0.673414]TJ /R19 9.96264 Tf EI Q )0.671944]TJ stream ET PHYSIQUE 2 MP 2019: L’indice et le froid ----CHIMIE MP 2019: Les batteries Lithium-Soufre ----PHYSIQUE 1 MP 2018: Interaction laser plasma à haut éclairement ----CHIMIE MP PSI 2018: Le bioéthanol ---- [(\()3.35237(q)-2.33195(u)1.3483(i)-336.588(c)-1.3336(a)-6.01515(l)0.671944(c)-1.3336(u)1.3483(l)0.671944(e)-326.549(l)0.671944(e)-1.3336(u)1.3483(r)-331.13(m)2.02465(o)18.0749(y)21.758(e)-1.3336(n)1.3483(n)1.34683(e)-1.33213(\))3.35237(. L'étude de la propagation des épidémies joue un rôle important dans les politiques de santé publique. [(f)4.35514(o)-6.01515(r)-5.91443(c)-1.33286(é)-1.33286(m)2.02392(e)-1.33286(n)25.4383(t)-225.502(e)-1.33286(n)25.4383(t)3.35237(i)0.671944(e)-1.3336(r)-5.91517(. Ce sujet est composé de deux problèmes indépendants, le premier de … 259.92 0 Td L’épreuve d’informatique du concours Mines-Ponts est commune à toutes les filières et se base sur le programme informatique obligatoire de maths sup maths spé. Q )0.673414]TJ [(n)25.4383(u)1.3483(l)0.671944(e)-1.33286(n)25.4383(t)-454.357(q)-2.33122(u)1.3483(a)-6.01515(s)-3.1377(i)0.671944(m)2.02465(e)-1.3336(n)25.4383(t)-442.313(d)1.3483(e)-1.3336(u)1.3483(x)-472.087(à)-451.68(d)1.3483(e)-1.3336(u)1.3483(x)-460.042(e)-1.3336(n)-468.407(c)-1.3336(a)-6.01515(s)-3.1377(c)-1.3336(a)-6.01515(d)1.34683(e)-1.33213(,)-444.992(s)-3.1377(a)-6.01368(u)1.34683(f)-453.355(u)1.34683(n)-456.363(d)1.34683(e)-459.042(c)22.7579(h)1.34683(a)-6.01368(q)-2.33195(u)1.34683(e)-459.042(c)-1.33213(ô)-6.01368(t)]TJ Chiffrer les données est nécessaire pour assurer la confidentialité lors d’échanges d’informations sensibles. /R10 8.96638 Tf [(l)0.673414(i)0.673414(s)-3.1377(a)-6.01368(t)3.35237(i)0.673414(o)-6.01368(n)-468.408(d)1.34683(e)-1.33213(s)-484.938(f)4.35514(o)-6.01368(n)1.34683(c)-1.33213(t)3.35237(i)0.673414(o)-6.01368(n)1.34683(s)-3.1377]TJ 8.33333 0 0 8.33333 0 0 cm BT /R29 9.96264 Tf q 3048 0 0 -5 436.9 252.9 cm 9.72 0 Td q Section PC. 258.96 0 Td [(M)1.02115(o)-6.01515(n)1.3483(m)2.02392(e)-1.33286(g)-6.01515(e)-459.043(\()3.3531(e)-1.33286(n)1.3483(s)-3.1377(e)-1.3336(i)0.671944(g)-6.01515(n)1.3483(a)-6.01515(n)25.4383(t)3.35237(-)-4.00961(c)22.7564(h)1.3483(e)-1.3336(r)-5.91517(c)22.7564(h)1.3483(e)-1.3336(u)1.3483(r)-427.49(à)-451.68(l)0.671944(')0.671944(u)1.3483(n)1.3483(i)0.671944(v)21.758(e)-1.33213(r)-5.91369(s)-3.1377(i)0.673414(t)3.35237(é)-1.33213(\))-454.358(e)-1.33213(t)-454.358(G)1.60267(u)1.34683(i)0.673414(l)0.673414(l)0.673414(a)-6.01368(u)]TJ /R48 9.96264 Tf Informatique - Autour des nombres premiers. 7.32 0 Td Vous trouverez ci-dessous les passages correspondant à l'anglais : 0 g )0.673414]TJ /R10 8.96638 Tf 1 0 0 1 80.04 405.96 Tm [(I)-2.69562(. q 105 0 0 -4 530.9 5164.9 cm /W 1 /R46 9.96264 Tf /R21 9.96264 Tf 9.96 0 Td 14737 /R19 9.96264 Tf /W 1 [(r)-5.91443(i)0.671944(s)-3.1377(q)-2.33122(u)1.3483(e)-314.504(d)1.3483(e)-338.594(m)2.02465(a)-6.01515(s)-3.1377(q)-2.33195(u)1.3483(e)-1.3336(r)-319.085(d)1.3483(e)-1.3336(s)-340.398(f)4.35514(o)-6.01515(n)1.3483(c)-1.3336(t)3.35237(i)0.671944(o)-6.01515(n)1.3483(s)-328.353(d)1.3483(é)-1.33213(j)4.35514(à)-343.274(e)-1.33213(x)-2.33195(i)0.673414(s)-3.1377(t)3.35237(a)-6.01368(n)25.4368(t)3.35237(e)-1.33213(s)-3.1377(. [(m)2.02392(a)-6.01515(t)3.3531(i)0.671944(q)-2.33122(u)1.3483(e)-338.593(q)-2.33122(u)1.3483(')0.671944(i)0.671944(l)-336.588(n)1.3483(')0.671944(e)-1.3336(s)-3.1377(t)-321.863(e)-1.3336(n)-335.912(r)-5.91517(é)-1.3336(a)-6.01515(l)0.671944(i)0.671944(t)3.35237(é)-169.964(! /BPC 1 Vous trouverez dans cette partie du site les sujets de Sciences de l'Ingénieur et d'Informatique des différents concours. ET [(4)-499.86(A)27.1167(t)3.3531(t)3.3531(e)-1.33286(n)25.4383(t)3.3531(i)0.671944(o)-6.01515(n)1.3483(,)0.671944]TJ Mines 2019. 43.68 0 Td q 4 0 0 -104 530.9 3461.9 cm 263.4 0 Td -158.4 -17.88 Td -236.88 -11.88 Td Q /R48 9.96264 Tf 8.33333 0 0 8.33333 0 0 cm BT q 6 0 Td [(,)-324.542(q)-2.33195(u)1.34683(i)-324.542(r)-5.91369(e)-1.33213(n)25.4368(v)21.758(o)-6.01368(i)0.673414(e)-314.502(l)0.673414(e)-326.547(n)1.34683(o)-6.01368(m)26.1132(b)1.34683(r)-5.91369(e)-314.502(d)1.34683(e)-1.33213]TJ [(g)-6.01368(o)-6.01368(r)-5.91369(i)0.673414(t)3.35237(h)1.34683(m)2.02318(e)-278.367(e)-1.33213(s)-3.1377(t)-285.728(d)1.34683(o)-6.01368(n)1.34683(n)1.34683(é)-1.33213(,)0.673414]TJ /R48 9.96264 Tf [(t)3.3531(r)-5.91443(e)-1.33286(m)2.02392(e)-1.33286(n)25.4383(t)3.3531(s)-3.1377(\))-321.862(e)-1.33286(t)3.3531]TJ [(ln)0.930723]TJ [(n)25.4368(t)3.35237(a)-6.01368(t)3.35237(i)0.673414(o)-6.01368(n)-287.733(d)1.34683(e)-1.33213(s)-304.263(n)1.34683(o)-6.01368(m)26.1132(b)1.34683(r)-5.91369(e)-1.33213(s)-3.1377]TJ ET /R19 9.96264 Tf Concours Mines-Ponts Le sujet d'anglais comprend deux questions (compréhension et expression) portant sur un article, et un thème (= traduction du français vers l'anglais). /BPC 1 Visitor Posts. [(])168.63(])]TJ /R31 8.96638 Tf -158.76 -19.68 Td 268.92 0 Td EI Q /R10 8.96638 Tf -256.08 -12 Td Ce sujet aborde plusieurs problèmes numériques liés aux nombres premiers, no-tamment leur génération et leur comptage. /R27 9.96264 Tf /IM true )1.25959]TJ 8.33333 0 0 8.33333 0 0 cm BT 0 g 1 0 0 1 230.16 674.04 Tm [(s)-3.1377(u)1.3483(r)-343.174(l)0.671944(e)-350.638(t)3.3531(e)-1.3336(s)-3.1377(t)-345.953(p)1.3483(r)-5.91517(o)-6.01515(b)1.3483(a)-6.01515(b)1.3483(i)0.671944(l)0.671944(i)0.671944(s)-3.1377(t)3.35237(e)-326.549(d)1.3483(e)-350.639(p)1.3483(r)-5.91517(i)0.671944(m)2.02465(a)-6.01515(l)0.671944(i)0.671944(t)3.35237(é)-338.594(d)1.34683(e)-350.637(F)86.5029(e)-1.33213(r)-5.91369(m)2.02318(a)-6.01368(t)3.35237(,)-336.587(e)-1.33213(s)-3.1377(t)-345.953(e)-1.33213(n)1.34683(s)-3.1377(u)1.34683(i)0.673414(t)3.35237(e)]TJ )-336.588(F)86.5029(a)-6.01515(i)0.671944(r)-5.91517(e)-338.594(e)-1.3336(n)-335.912(s)-3.1377(o)-6.01515(r)-5.91517(t)3.35237(e)-338.594(d)1.3483(e)-350.639(m)2.02465(i)0.671944(n)1.3483(i)0.673414(m)2.02318(i)0.673414(s)-3.1377(e)-1.33213(r)-343.174(l)0.673414(e)-1.33213(s)-340.398(i)0.673414(m)2.02318(p)1.34683(r)-5.91369(é)-1.33213(c)-1.33213(i)]TJ 268.56 0 Td 17.76 0 Td 12.24 0 Td Mines-Ponts MP 2019 Informatique Epreuve, Concours Commun Mines Ponts (CCMP), Concours Informatique MP, AlloSchool 170.04 0 Td ID -273.36 -12 Td /R10 8.96638 Tf /R19 9.96264 Tf ET Ils sont publiés sur ce site selon les termes de la licence : Licence Creative Commons Attribution - Pas d’Utilisation Commerciale - Pas de Modification 3.0 France. q -286.68 -12 Td Concours commun Mines-Ponts 2019 ... Enoncé / Corrigé Mines 2019. BI [(\r)-3.51656]TJ 1 0 0 1 409.56 674.04 Tm endstream 6.6 0 Td ID Deuxièmesannées LycéeMasséna Mines-Ponts 19 : Corrigé Partie I. Préliminaires Question 1. /R19 9.96264 Tf Q q [(l)0.671944(e)-1.33286(m)2.02392(e)-1.33286(n)25.4383(t)-333.907(ê)-1.3336(t)3.35237(r)-5.91517(e)-326.549(i)0.671944(m)2.02465(p)1.3483(l)0.671944(é)-1.3336(m)2.02465(e)-1.3336(n)25.4383(t)3.35237(é)-1.3336(e)-1.3336(. 32.04 0 Td Q On appelle ces opérations « fonctions à sens unique ». [(1)-6.01515(2)-499.86(N)3.02669(e)-471.088(p)1.3483(a)-6.01515(s)-472.893(o)-6.01515(u)1.3483(b)1.3483(l)0.671944(i)0.671944(e)-1.3336(r)-475.67(d)1.3483(')0.671944(i)0.671944(m)2.02465(p)-22.7417(o)-6.01515(r)-5.91517(t)3.35237(e)-1.3336(r)-475.67(l)0.671944(e)-1.3336(s)-472.893(m)2.02465(o)-30.1051(d)1.3483(u)1.3483(l)0.671944(e)-1.3336(s)-484.938(n)1.34683(é)-1.33213(c)-1.33213(e)-1.33213(s)-3.1377(s)-3.1377(a)-6.01368(i)0.673414(r)-5.91369(e)-1.33213(s)-448.803(à)-475.769(l)0.673414(')0.673414(u)1.34683(t)3.35237(i)]TJ /IM true T*[(f)-5.10869(r)-5.10869(o)-5.10869(m)-510.999(m)-5.10869(a)-5.10869(t)-5.10869(h)-510.999(i)-5.10869(m)-5.10942(p)-5.10942(o)-5.10942(r)-5.10942(t)-498.954(l)-5.10942(o)-5.10942(g)-5.10942(,)-511(s)-5.10942(q)-5.10942(r)-5.10942(t)-5.10942(,)-511(f)-5.10942(l)-5.10942(o)-5.10942(o)-5.10942(r)-5.10942(,)-498.954(c)-5.10795(e)-5.10795(i)-5.10795(l)-5.10795]TJ )2.92107(f)2.92107(r)2.92107]TJ EI Q q 0.12 0 0 0.12 0 0 cm /R19 9.96264 Tf /R10 8.96638 Tf /R31 8.96638 Tf Q [(I)-0.330826(l)-348.633(n)1.3483(')0.671944(y)-339.591(a)-343.275(p)1.3483(a)-6.01515(s)-340.398(l)0.671944(i)0.671944(e)-1.3336(u)-335.912(d)1.3483(e)-350.639(s)-3.1377(e)-338.594(l)0.671944(a)-6.01515(i)0.671944(s)-3.1377(s)-3.1377(e)-1.3336(r)-331.13(i)0.671944(n)25.4383(t)3.35237(i)0.671944(m)2.02465(i)0.671944(d)1.3483(e)-1.3336(r)-343.175(p)1.34683(a)-6.01368(r)-343.174(l)0.673414(e)-338.592(t)3.35237(h)1.34683(è)-1.33213(m)2.02318(e)-1.33213(,)-348.632(l)0.673414(')0.673414(é)-1.33213(n)1.34683(o)-6.01368(n)1.34683(c)]TJ /R31 8.96638 Tf q 0.12 0 0 0.12 0 0 cm L’utilisation, la dup lication ou la révélation par le gouvernement des Etats-Unis sont soumises aux restrictions énoncées dans la section FAR 52.227-19 (Logiciel informatique commercial - Droits limités) et la section DFARS
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