Question

In: Advanced Math

Let p be the prime number (2^20)*(3^7)5 + 1 = 11466178561. Solve for x such that...

Let p be the prime number (2^20)*(3^7)5 + 1 = 11466178561. Solve for x such that 2^x ≡ 2376886429 (mod p) Explain your method carefully.

Expert Solution

GIVEN DATA FROM THE PROBLEM

220 * 37 * 5 + 1 = 11466178561

2^x ≡ 2376886429 (mod p)

SOLVING FOR X :

AS WE HAVE

is a prime number so it is odd as bevause if then the system has no solution as we have the theorem has a solution if and only if divides .

So is odd and so is even and so .

Now ,

, as .

where .

Hence the required solution of the given congruence are given by ,

Colby Messinger answered 2 years ago

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