/*****************************************************************************/ /* */ /* COUNT PAIRS OF CONSECUTIVE ROOTS OF THE CONGRUENCE X**((P-1)/N)=Y(MOD P) */ /* 06/01/07 (dkc) */ /* */ /* This C program tests propositions for n=8. */ /* */ /*****************************************************************************/ #include <stdio.h> #include <math.h> #include "input.h" unsigned int croots(unsigned int *input, unsigned int index, unsigned int n, unsigned int *output); void res64_32(unsigned int exp0, unsigned int exp1, unsigned int q0, unsigned int q1, unsigned int *output, unsigned int base); unsigned int r[100000]; unsigned int U[2]; int main () { unsigned int n=8; // n value unsigned int h,i,sum,p,p1,pn,flag0,flag1,temp,count; unsigned int s[14]; FILE *Outfp; Outfp = fopen("out8.dat","w"); count=0; for (h=0; h<insize; h++) { p=input[2*h]; // load p if (p>40000) // reduce execution time break; i=croots(input, h, n, s); // count consecutive roots of congruences if (i==0) // continue if n does not divide p-1 continue; if (i==2) { printf(" error: bad primitive root \n"); break; } printf(" p=%d ",input[2*h]); /***************************************************/ /* check if the sum of S[i] is equal to (p-1)/n-1 */ /***************************************************/ sum=0; for (i=0; i<n; i++) { sum=sum+s[i]; printf(" %d ",s[i]); } printf("\n"); p1=p-1; pn=p1/n; if (sum!=pn-1) { printf(" error: incorrect sum \n"); break; } /**********************************/ /* check if s[1]=s[3]=s[5]=s[7] */ /**********************************/ flag0=0; if ((s[0]==s[2])&&(s[2]==s[4])&&(s[4]==s[6])) { if ((s[1]==s[3])&&(s[3]==s[5])&&(s[5]==s[7])) flag0=1; } /***********************************/ /* check if (p-1)/n is a square */ /***********************************/ flag1=0; temp=(unsigned int)(sqrt((double)pn)+0.01); if (temp*temp==pn) flag1=1; /****************************************************************/ /* check if (p-1)/n is an odd square when s[1]=s[3]=s[5]=s[7] */ /****************************************************************/ if (flag0==1) { fprintf(Outfp," p=%d ",p); for (i=0; i<n; i++) fprintf(Outfp," %d ",s[i]); fprintf(Outfp,"\n"); if ((flag1==0)||((pn/2)*2==pn)) { fprintf(Outfp,"p=%d, error: (p-1)/n is not an odd square \n",p); printf(" error: (p-1)/n is not an odd square \n"); } } /*****************************************************************************/ /* check if s[1]=s[3]=s[5]=s[7] when pn is odd square and 2**(2*r)=1(mod p) */ /*****************************************************************************/ if (flag1==1) { if ((pn/2)*2!=pn) { res64_32(0, pn*2, 0, p, U, 2); if ((U[0]==0)&&(U[1]==1)) { if (flag0==0) { fprintf(Outfp,"p=%d, error: unequal s values \n",p); printf(" error: unequal s values \n"); } } } } /******************************************************************/ /* check if s[1]=s[3] when 2**(2*r)=1(mod p) and (p-1)/n is odd */ /******************************************************************/ if ((pn/2)*2!=pn) { res64_32(0, pn*2, 0, p, U, 2); if ((U[0]==0)&&(U[1]==1)) { if ((s[0]!=s[2])||(s[4]!=s[6])) { fprintf(Outfp,"p=%d, error: unequal s values \n",p); printf(" error: unequal s values \n"); } } } /******************************************************************************/ /* check if s[1]=s[3]=s[5]=s[7] when 2**(2*r)<>1(mod p) and (p-1)/n is even */ /******************************************************************************/ if ((pn/2)*2==pn) { res64_32(0, pn*2, 0, p, U, 2); if ((U[0]!=0)||(U[1]!=1)) { if ((s[0]!=s[2])||(s[4]!=s[6])||(s[2]!=s[4])) { fprintf(Outfp,"p=%d, error: unequal s values \n",p); printf(" error: unequal s values \n"); } } /*****************************************************************************/ /* check if s[1]-s[3]=s[5]-s[7] when 2**(2*r)=1(mod p) and (p-1)/n is even */ /*****************************************************************************/ else { if ((s[0]-s[2])!=(s[4]-s[6])) { fprintf(Outfp,"p=%d, error: unequal differences \n",p); printf(" error: unequal differences \n"); } } } } fclose(Outfp); return(0); }