MathDB

Suppose that the following equations hold for positive integers

x

y

, and

n

, where

n>18

: \begin{align*} x+3y&\equiv7\pmod{n}\\ 2x+2y&\equiv18\pmod{n}\\ 3x+y&\equiv7\pmod{n} \end{align*} Compute the smallest nonnegative integer

a

such that

2x\equiv a\pmod{n}

Problem Statement