Sz\303\241m\303\255t\303\263g\303\251pes sz\303\241melm\303\251let J\303\241rai Antal Ezek a programok csak szeml\303\251ltet\303\251sre szolg\303\241lnak

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

restart; with(numtheory);

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

n:=nextprime(7*10^2)*prevprime(14*10^2);

IicqcCEpKg==

B:=20; F:=[]; for j from 2 while j<B do if isprime(j) then F:=[op(F),j]; fi; od; F; nops(F);

IiM/

NyI=

NyoiIiMiIiQiIiYiIigiIzYiIzgiIzwiIz4=

IiIp

rnd:=rand(2..n-2); rnd(); ifactors(%^2 mod n);

Zio2IkYjRiNGIywmLWYqRiNGIzYjSShidWlsdGluR0YjRiMiJCRSRiNGI0YjSSVGQUlMRyUqcHJvdGVjdGVkRzYlIiInIicncCEpKiIjPyIiIiIiI0YwRiNGI0Yj

IictTjY=

NyQiIiI3JTckIiIjRiY3JCIiJkYjNyQiJig0N0Yj

R:=[]; while nops(R)<nops(F)+5 do x:=rnd(); y:=ifactors(modp(x^2,n))[2]; if y[nops(y)][1]>=B then next else R:=[op(R),[x,y]] fi; od:

NyI=

R;

Ny83JCInZFslKTcnNyQiIiNGJzckIiImIiIiNyQiIihGJzckIiM4Rio3JCIjPEYqNyQiJ2JYUTclNyRGJ0YqNyQiIzZGKjckRi5GJzckIidwLHY3JkY0RihGNTckIiM+Rio3JCInJj5kIzcmNyRGJyIiKjckIiIkRio3JEYsRipGLTckIidDdSgpNyY3JEYnRixGQjckRilGQ0YtNyQiJD8jNyU3JEYnIiIlNyRGKUYnNyRGNkYnNyQiJ1ooMyo3JUY0NyRGNkZDNyRGPEYnNyQiJnlGIjcmRjQ3JEYpRilGREY1NyQiJ0U7NzcmNyRGJyIiJzckRkNGJ0YoRkQ3JCInczZgNyc3JEYnRik3JEZDRkNGKEZERi83JCInck1YNyVGQEZERjU3JCImdjkjNyZGaW5GKDckRjBGJ0Y7NyQiJyQ9Yik3JkZNNyRGQ0ZORihGKw==

Rc:=[[21475, [[3, 2], [5, 1], [17, 2], [19, 1]]], [855183, [[2, 4], [3, 4], [5, 1], [7, 2]]], [164912, [[3, 1], [5, 2], [11, 1], [13, 1], [19, 1]]], [728436, [[2, 1], [3, 2], [11, 1], [13, 1], [17, 1]]], [362222, [[3, 2], [19, 1]]], [297430, [[5, 1], [19, 4]]], [744161, [[3, 3], [5, 1], [11, 1], [13, 1], [19, 1]]], [495370, [[2, 8], [3, 6], [5, 1]]], [577106, [[2, 1], [11, 1], [13, 2], [19, 1]]], [699549, [[7, 4]]], [689811, [[5, 4], [13, 1], [17, 1]]], [695704, [[3, 2], [5, 1], [11, 4]]], [315384, [[2, 4], [3, 1], [5, 1], [11, 1], [13, 1], [19, 1]]]];

Ny83JCImdjkjNyY3JCIiJCIiIzckIiImIiIiNyQiIzxGKDckIiM+Ris3JCInJD1iKTcmNyRGKCIiJTckRidGNEYpNyQiIihGKDckIic3XDs3JzckRidGKzckRipGKDckIiM2Ris3JCIjOEYrRi43JCInTyVHKDcnNyRGKEYrRiZGPUY/NyRGLUYrNyQiJ0FBTzckRiZGLjckIidJdUg3JEYpNyRGL0Y0NyQiJ2hUdTcnNyRGJ0YnRilGPUY/Ri43JCIncWBcNyU3JEYoIiIpNyRGJyIiJ0YpNyQiJzFyZDcmRkRGPTckRkBGKEYuNyQiJ1wmKnA3IzckRjdGNDckIic2KSpvNyU3JEYqRjRGP0ZFNyQiJy9kcDclRiZGKTckRj5GNDckIiclUTokNyhGM0Y7RilGPUY/Ri4=

with(linalg);

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

RM:=matrix(nops(R),nops(F),0);

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

for i to nops(Rc) do v:=Rc[i][2]; for j to nops(v) do vv:=v[j]; for k to nops(F) do if vv[1]=F[k] then RM[i,k]:=vv[2] fi od; od; od: print(RM);

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

x:=Rc[10][1]; y:=7^2; x^2-y^2 mod n;

IidcJipw

IiNc

IiIh

igcd(n,x-y);

IiUqUiI=

RM:=addrow(RM,4,9,1);

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

RM:=addrow(RM,3,7,1): RM:=addrow(RM,3,13,1);

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

RM:=addrow(RM,2,1,1): RM:=addrow(RM,2,6,1): RM:=addrow(RM,2,7,1): RM:=addrow(RM,2,8,1): RM:=addrow(RM,2,12,1):RM:=addrow(RM,2,13,1);

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

RM:=addrow(RM,1,5,1): RM:=addrow(RM,1,9,1);

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

x:=Rc[5][1]*(Rc[1][1]*Rc[2][1]) mod n;

IidCMnM=

y:=2^2*3^4*5*7*17*19 mod n;

IidCMnM=

x^2-y^2 mod n;

IiIh

igcd(n,x-y);

IicqcCEpKg==

;

n:=nextprime(7*10^5)*prevprime(14*10^5);

Ii0qKioqcCsrKSo=

n mod 8; n:=23*n; n mod 8;

IiIo

Ii94Kio0OythQQ==

IiIi

m:=2000; B:=50; T:=2.; b:=ceil(sqrt(n)); F:=[[2,floor(0.5+2.*log[2.](2)),1]]; for j from 3 while j<B do if isprime(j)=false then next fi; if jacobi(n,j)=1 then F:=[op(F),[j,floor(0.5+j/(j-1)*log[2.](j)),msqrt(n,j)]]; fi; od; F; nops(F);

IiUrPw==

IiNd

JCIiIyIiIQ==

IihMd3Ul

NyM3JSIiI0YkIiIi

Nyk3JSIiI0YkIiIiNyUiIiRGJEYlNyUiIzgiIiUiIiY3JSIjPkYqIiInNyUiI0hGKyIjNzclIiNKRitGMTclIiNQRisiIzU=

IiIo

S:= rtable(0..2*m,0);

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

p:=F[1][1]; lp:=F[1][2]; x:=modp(m-b+F[1][3],p); while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od:

IiIj

IiIj

IiIi

for j from 2 to nops(F) do ppp:=F[j]; p:=ppp[1]; lp:=ppp[2]; x:=modp(m-b+ppp[3],p); while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od: x:=modp(m-b-ppp[3],p); while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od: od: R:=[]; TT:=floor(log[2.](2*m*b)/T);

NyI=

IiM8

for j from 0 to 2*m do if S[j]>=TT then R:=[op(R),j-m] fi od: R;

NywhJSs9ISUvNiEkJWUhJEslISQ7IiEiIyIlbTgiJTE6IiU5PCIlTTw=

map(y->ifactors((y+b)^2-n),R);

Nyw3JCEiIjcpNyQiIiMiIiQ3JEYoIiIiNyQiIz5GKjckIiNIRio3JCIjSkYqNyQiI3JGKjckIiQoZUYqNyRGJDcoRiZGKTckIiM4RipGK0YtNyQiJmA0J0YqNyRGJDcpRiZGKUY3RitGLzckIiNgRio3JCIkcCZGKjckRiQ3KEYmRilGK0YtNyQiI1BGKjckIiV4JClGKjckRiQ3KDckRiciIihGKUY3RitGQzckIiQ4JEYqNyRGJDcoRiY3JEYoRidGN0YrRi1GLzckRio3KUYmRk9GN0YrRi03JCIkUiJGKjckIiQiPUYqNyRGKjcpNyRGJyIiJkYpRjdGK0YtRjE3JCIkJEhGKjckRio3KDckRiciIidGKUY3Ri1GQzckIiV6Z0YqNyRGKjcoRiY3JEYoRihGK0YvRkM3JCIlKlwkRio=

n:=nextprime(7*10^7)*prevprime(14*10^7);

IjFkKCoqKlxKKyspKg==

n mod 8; n:=37*n; n mod 8;

IiIm

IjM0NSoqXGw2K0VP

IiIi

m:=10000; B:=100; T:=1.5; F:=[[2,floor(0.5+2.*log[2.](2)),1]]; for j from 3 while j<B do if isprime(j)=false then next fi; if jacobi(n,j)=1 then F:=[op(F),[j,floor(0.5+j/(j-1)*log[2.](j)),msqrt(n,j)]]; fi; od; F; nops(F);

IiYrKyI=

IiQrIg==

JCIjOiEiIg==

NyM3JSIiI0YkIiIi

Ny83JSIiI0YkIiIiNyUiIiYiIiRGJDclIiIoRihGJDclIiM4IiIlRiU3JSIjPkYtRio3JSIjQkYnIiM2NyUiI0hGJ0YyNyUiI1RGJyIjOTclIiNaIiInRi03JSIjYEY6RjI3JSIjZkY6IiNBNyUiI3JGOiIiKTclIiMoKkYqIiNu

IiM4

dd:=floor((2*n/m^2)^(1/4.)): if type(dd,odd) then dd:=dd+1; fi: dd:=dd..dd;

OyIkI0hGIw==

if abs(op(1,dd)-(2*n/m^2)^(1/4.))<abs(op(2,dd)-(2*n/m^2)^(1/4.)) then d:=prevprime(op(1,dd)); while modp(d,4)<>3 or jacobi(d,n)<>1 do d:=prevprime(d); od; dd:=d..op(2,dd); else d:=nextprime(op(2,dd)); while modp(d,4)<>3 or jacobi(d,n)<>1 do d:=nextprime(d); od; dd:=op(1,dd)..d; fi: d; dd;

IiQ2JA==

OyIkciMiJDYk

a:=d^2; h0:=n&^((d-3)/4) mod d;

IiZAbio=

IiNg

h1:=n*h0 mod d; (n-h1^2)/d; h2:=%*h0*((d+1)/2) mod d;

IiRCIw==

IjEhW3NNeDtmOyI=

IiNE

b:=mods(h1+h2*d,a); b^2-n mod a; c:=(b^2-n)/a;

IiUpKno=

IiIh

IS4wOWBHKltQ

S:= rtable(0..2*m,0); p:=F[1][1]; lp:=F[1][2]; x:=modp(m+(-b+F[1][3])/a,p); while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od:

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

IiIj

IiIj

IiIi

for j from 2 to nops(F) do ppp:=F[j]; p:=ppp[1]; lp:=ppp[2]; x:=modp(m+(-b+ppp[3])/a,p); while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od: x:=modp(m+(-b-ppp[3])/a,p); while x<=2*m do S[x]:=S[x]+lp; x:=x+p; od: od: R:=[]; TT:=floor(log[2.](a*m^2/2.)/T);

NyI=

IiNH

for j from 0 to 2*m do if S[j]>=TT then R:=[op(R),j-m] fi od: R;

NyUiJTo3IiVERSIlQ1M=

map(y->ifactors(a*y^2+2*b*y+c),R);

NyU3JCEiIjcqNyQiIiMiIiQ3JCIiJiIiIjckIiIoRis3JCIjPkYrNyQiI1RGKzckIiNaRis3JCIjYEYrNyQiJVBtRis3JEYkNyk3JEYnIiM3Rik3JCIjQkYrNyQiI1BGK0YyRjQ3JCIjckYrNyRGJDcqRilGLEYuRjxGMkY0NyQiI2ZGKzckIiRyKkYr

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn