Square Modulo 5/Corollary
Jump to navigation
Jump to search
Theorem
When written in conventional base $10$ notation, no square number ends in one of $2, 3, 7, 8$.
Proof
The absence of $2$ and $3$ from the digit that can end a square follows directly from Square Modulo 5.
As $7 \equiv 2 \pmod 5$ and $8 \equiv 3 \pmod 5$, the result for $7$ and $8$ follows directly.
$\blacksquare$
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 14$: Worked Example $1$: Congruence modulo $m$ ($m \in \N$)