- #1

Shackleford

- 1,656

- 2

## Homework Statement

For what values of

*a*(mod 78) will

*ax*≡ 26 (mod 78) have exactly 13 solutions?

## Homework Equations

gcd, etc.

## The Attempt at a Solution

A solutions exists if gcd(a,n) | b.

gcd(a, 78) | b

Let d = gcd(a, n). If d|b, then ax ≡ b (mod n) has exactly d solutions.

I want to set d = 13 = gcd(a, 78) and 13 | 78.

I know this is a simple problem, but I'm obviously missing something.