Show that square of any odd natural number is congruent to 1 mod 8.
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
19071
solution set for congruence $x^2 \equiv 1 \mod m$
80875
Congruence equation ...
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
131941
Solve quadratic congruences.
20443
Calculate sum of squares of first $n$ odd numbers
149481
Number theory counting sums of squares modulus
6918
Primes congruent to 1 mod 6
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
31064
Showing $x^8\equiv 16 \pmod{p}$ is solvable for all primes $p$
47720
Isomorphism from Natural numbers to the Odd Natural numbers
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
21108
Perfect squares and modularly congruency in mod 5