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10 ' r_int.ub 20 ' y2=x3+ax+b , 4a3+27b2<>0 30 Va%=9*7*11*13:Vb%=128*5*17:Vc%=2^2*3^2*5^2:Vd%=7*11*13:Ex=10000 40 dim A%(Va%-1),B%(Vb%-1),C%(Vc%),D%(Vc%),E%(Vd%) 50 for I%=0 to Va%-1:A%(I%)=1:next I% 60 for I%=0 to Va%\2+1:A%(I%^2@Va%)=0:next I% 70 for I%=0 to Vb%-1:B%(I%)=1:next I% 80 for I%=0 to Vb%\2+1:B%(I%^2@Vb%)=0:next I% 90 for I%=0 to Vc%-1:C%(I%)=1:next I% 100 for I%=0 to Vc%\2+1:C%(I%^2@Vc%)=0:next I% 110 print "search the integer points x <= 100,000,000" 120 print "y2 = x3 + ax + b : input a, b" 130 input "a=";A:input "b=";B 140 D=4*A^3+27*B^2:if D=0 then print "not irreducible":goto 120 150 print "a=";A;", b=";B;", discriminant=";D:F%=0 160 clr time 170 ' 180 X=-Ex 190 U=X^3+A*X+B:V=3*X^2+A 200 if V=0 then Sx=1:goto 230 else W=U/V 210 if abs(W)>0.5 then X=X-W:goto 190 220 Sx=int(X):if Sx<-Ex then Sx=-Ex 230 J%=0 240 for I%=0 to Vd%-1:W=I%^3+A*I%+B 250 if I%>=Vc% then 290 260 if C%(W@Vc%)=1 then 290 270 inc J%:D%(J%)=I% 280 ' 290 E%(I%)=kro(W,Vd%) 300 next I% 310 ' 320 Base=Vc%*(Sx\Vc%):if Base<0 then Base=Base-Vc% 330 for I%=1 to J%:X=Base+D%(I%) 340 if E%(X@Vd%)=-1 then 400 350 Y2=X^3+A*X+B:if Y2<0 then 400 360 if B%(Y2@Vb%)=1 then 400 370 if A%(Y2@Va%)=1 then 400 380 Y=isqrt(Y2):if res>0 then 400 390 inc F%:R%=fnSub(X,Y) 400 next I% 410 Base=Base+Vc%:if Base<100000000 then 330 420 print time1000/1000 430 end 440 ' 450 fnSub(X,Y) 460 local C%,M,X1,Y1,Xn,Yn 470 print F%;": (";X;",";Y;")"; 480 if Y=0 then print " order 2":return(0) 490 C%=2 500 M=(3*X^2+A)//(2*Y):if den(M)<>1 then print:return(0) 510 X1=M^2-2*X:Y1=M*(X-X1)-Y:print:print spc(4);"2P = (";X1;",";Y1;")"; 520 if and{X=X1,Y=(-Y1)} then print " order";C%+1:return(0) 530 M=(Y1-Y)//(X1-X):if den(M)<>1 then print:return(0) 540 Xn=M^2-X-X1:Yn=M*(X-Xn)-Y:inc C%:X1=Xn:Y1=Yn 550 print:print spc(4);cutspc(str(C%));"P = (";X1;",";Y1;")"; 560 goto 520