Congruence Modulo Integer/Examples/531 not equiv 1236 mod 7561
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:
\(\ds \size {531}\) | \(<\) | \(\ds \dfrac {7561} 2\) | ||||||||||||
\(\ds \size {1236}\) | \(<\) | \(\ds \dfrac {7561} 2\) |
From Congruent Integers less than Half Modulus are Equal, it follows that $531 = 1236$.
The result follows by Proof by Contradiction.
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {4-1}$ Basic Properties of Congruences: Exercise $7 \ \text{(d)}$