/*****************************************************************************/ /* */ /* FACTOR (d**p + e**p)/(d + e) */ /* 11/13/06 (dkc) */ /* */ /* This C program finds d and e such that (d**p + e**p)/(d + e) is a cube */ /* or p times a cube. p is set to 3. */ /* */ /*****************************************************************************/ #include <stdio.h> #include <math.h> #include "table0c.h" unsigned int lmbd(unsigned int mode, unsigned int a); void sum(unsigned int *addend, unsigned int *augend); void differ(unsigned int *minuend, unsigned int *subtrahend); void bigprod(unsigned int a, unsigned int b, unsigned int c, unsigned int *p); void quotient(unsigned int *a, unsigned int *b, unsigned int); int main () { int p=3; // input prime int dbeg=10000; // starting "a" value int dend=1; // ending "a" value //int stop=0x2e831; int sumdif=1; // select [(a**p+b**p)/(a+b)] if "sumdif" is non-zero, // or [(a**p-b**p)/(a-b)] otherwise extern unsigned short table3[]; extern unsigned int output[]; extern unsigned int error[]; int t3size=2556; int outsiz=1999; int n=0; int d,e,a,b,temp; int i,j,k,l,lp,m; unsigned int S[2],T[2],V[2],X[3]; double croot2,croot4,halfcr4; FILE *Outfp; Outfp = fopen("output.dat","w"); croot2=1.259921; croot4=1.587401; halfcr4=croot4*((double)(0.5)); /***********************************/ /* factor (d**p + e**p)/(d + e) */ /***********************************/ error[0]=0; // clear error array for (d=dbeg; d>=dend; d--) { for (e=d-1; e>0; e--) { // if (e!=stop) continue; /*******************************/ /* check for common factors */ /*******************************/ if((d==(d/2)*2)&&(e==(e/2)*2)) continue; if((d==(d/3)*3)&&(e==(e/3)*3)) continue; if((d==(d/5)*5)&&(e==(e/5)*5)) continue; if((d==(d/7)*7)&&(e==(e/7)*7)) continue; /***********************/ /* Euclidean G.C.D. */ /***********************/ a=d; b=e; if (b>a) { temp=a; a=b; b=temp; } loop: temp = a - (a/b)*b; a=b; b=temp; if (b!=0) goto loop; if (a!=1) continue; /************************************/ /* compute (d**p + e**p)/(d + e) */ /************************************/ S[0]=0; S[1]=d; for (i=0; i<p-1; i++) { bigprod(S[0], S[1], d, X); S[0]=X[1]; S[1]=X[2]; } T[0]=0; T[1]=e; for (i=0; i<p-1; i++) { bigprod(T[0], T[1], e, X); T[0]=X[1]; T[1]=X[2]; } if (sumdif==1) { sum(S, T); temp=d+e; if (((d+e)/p)*p==(d+e)) temp=temp*p; quotient(T, S, temp); } else { differ(S, T); temp=d-e; if (((d-e)/p)*p==(d-e)) temp=temp*p; quotient(T, S, temp); } /************************************************/ /* look for prime factors using look-up table */ /************************************************/ if (S[0]==0) l = 32 - lmbd(1, S[1]); else l = 64 - lmbd(1, S[0]); j=l-(l/3)*3; l=l/3; l = 1 << l; if (j==0) lp=(int)(((double)(l))*halfcr4); if (j==1) { lp=l; l=(int)(((double)(l))*croot2); } if (j==2){ lp=(int)(((double)(l))*croot2); l=(int)(((double)(l))*croot4); } lp=lp-1; l=l+1; if (l>table3[t3size-1]) { error[0]=5; goto bskip; } else { j=0; for (i=0; i<t3size; i++) { if (table3[i] < lp) j=i; else break; } k=j; for (i=j; i<t3size; i++) { if (table3[i] < l) k=i; else break; } } for (i=j; i<=k; i++) { m=0; l = table3[i]; quotient(S, V, l); bigprod(V[0], V[1], l, X); if ((S[0]!=X[1]) || (S[1]!=X[2])) continue; aloop: S[0]=V[0]; S[1]=V[1]; m=m+1; quotient(S, V, l); bigprod(V[0], V[1], l, X); if ((S[0]==X[1]) && (S[1]==X[2])) goto aloop; if ((m/3)*3!=m) goto askip; } if ((S[0]!=0) || (S[1]!=1)) continue; if (n+1>outsiz) { error[0]=6; goto bskip; } output[n]=d; output[n+1]=e; n=n+2; askip:temp=0; } } bskip: output[n]=-1; fprintf(Outfp," error=%d \n",error[0]); fprintf(Outfp," count=%d \n",(n+1)/3); for (i=0; i<(n+1)/2; i++) fprintf(Outfp," %#10x %#10x \n",output[2*i],output[2*i+1]); fclose(Outfp); return(0); }