# Congruence Modulo Integer/Examples/531 not equiv 1236 mod 7561

## Example of Non-Congruence Modulo an Integer

$531 \not \equiv 1236 \pmod {7561}$

## Proof

Aiming for a contradiction, suppose $531 \equiv 1236 \pmod {7561}$.

We have that:

 $\displaystyle \size {531}$ $<$ $\displaystyle \dfrac {7561} 2$ $\displaystyle \size {1236}$ $<$ $\displaystyle \dfrac {7561} 2$

From Congruent Integers less than Half Modulus are Equal, it follows that $531 = 1236$.

The result follows by Proof by Contradiction.

$\blacksquare$