Find the smallest strong pseudoprime to the base 3 in the interval [700, 800]. Kindly show all trials without using any programming language code.
code in cpp:
#include <bits/stdc++.h>
using namespace std;
// Function to check if the given number is composite
bool checkcomposite(int n)
{
// Check if there is any divisor of n less than
sqrt(n)
for (int i = 2; i <= sqrt(n); i++) {
if (n % i == 0)
return 1;
}
return 0;
}
// Effectively calculate (x^y) modulo mod
int power(int x, int y, int mod)
{
// Initialize result
int res = 1;
while (y) {
// If power is odd, then update
the answer
if ((y %2)== 1)
res = (res * x)
% mod;
// Square the number and
reduce
// the power to its half
y = y >> 1;
x = (x * x) % mod;
}
// Return the result
return res;
}
// Function to check for Fermat(strong) Pseudoprime
bool Check(int n, int a)
{
// If it is composite and satisfy Fermat
criterion
if (a>1 && checkcomposite(n) &&
power(a, n - 1, n) == 1)
return 1;
// Else return 0
return 0;
}
int main()
{
int a=3;//to the base which we want to find
// Function call
for(int i=700;i<=800;i++){
if(Check(i, a)){
cout<<i<<endl;
break;
}
}
output:-
return 0;
}
Find the smallest strong pseudoprime to the base 3 in the interval [700, 800]. Kindly show...
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Hello, please kindly show all your steps without skipping any
part. Please also cite any defintions if necessary generously to
help me understand this question. Thanks in advance.
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Please show steps with explanations
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