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

From ProofWiki
Jump to navigation Jump to search

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.

$\blacksquare$


Sources