﻿ test propositions for n=3
```/*****************************************************************************/
/*									     */
/*  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=3.				     */
/*									     */
/*****************************************************************************/
#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];
int main () {
unsigned int n=3;		 // n value
unsigned int h,i,sum,p,p1,pn,temp,flag0,flag1,flag2;
unsigned int s[14];
unsigned int U[2];
FILE *Outfp;
Outfp = fopen("out3.dat","w");
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[2]=s[2]-s[3]   */
/***********************************/
flag0=0;
if ((s[0]-s[1])==(s[1]-s[2]))
flag0=1;
if ((s[1]-s[0])==(s[0]-s[2]))
flag0=1;
/****************************/
/*  check if r is a square  */
/****************************/
flag1=0;
temp=(unsigned int)(sqrt((double)pn)+0.01);
if (temp*temp==pn)
flag1=1;
/************************************/
/*  check if s[3]-s[2]+2=s[1]-s[3]  */
/************************************/
flag2=0;
if ((2*s[2]+2)==(s[0]+s[1]))
flag2=1;
/*****************************************************/
/* check if r is a square when s[1]-s[2]=s[2]-s[3]   */
/*****************************************************/
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) {
fprintf(Outfp,"p=%d, error: (p-1)/n is not a square \n",p);
printf(" error: (p-1)/n is not a square \n");
}
}
/*******************************************************/
/* check if r is a square when s[3]-s[2]+2=s[1]-s[3]   */
/*******************************************************/
if (flag2==1) {
if (flag1==0) {
fprintf(Outfp,"p=%d, error: (p-1)/n is not a square \n",p);
printf(" error: (p-1)/n is not a square \n");
}
}
/***********************************************************************/
/* check if s[1]-s[2]=s[2]-s[3] when r is a square and 2**r<>1(mod p)  */
/***********************************************************************/
if (flag1==1) {
res64_32(0, pn, 0, p, U, 2);
if ((U[0]!=0)||(U[1]!=1)) {
if (flag0==0) {
fprintf(Outfp,"p=%d, error: differences not equal \n",p);
printf(" error: differences not equal \n");
}
}
/*************************************************************************/
/* check if s[3]-s[2]+2=s[1]-s[3] when r is a square and 2**r==1(mod p)  */
/*************************************************************************/
else {
if (flag2==0) {
fprintf(Outfp,"p=%d, error: differences not equal \n",p);
printf(" error: differences not equal \n");
}
}
}
/****************************************/
/*  check if r/2 is odd when s[1]=s[3]	*/
/****************************************/
if ((s[0]==s[2])||(s[1]==s[2])) {
if ((pn/4)*4==pn) {
fprintf(Outfp,"p=%d, error: r/2 is even \n",p);
printf(" error: r/2 is even \n");
}
}
/*************************/
/*  check if s[1]=s[2]	 */
/*************************/
if (s[0]==s[1]) {
fprintf(Outfp,"p=%d, error: s[1] equals s[2] \n",p);
printf(" error: s[1] equals s[2] \n");
}
}
fclose(Outfp);
return(0);
}
```