Show that if $n$ is odd and isn't divisible by $3$ then $n^2 \equiv 1 (\bmod 24)$
15915
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
48053
Show that 13 divides $2^{70}+3^{70}$
31895
Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
139659
Find all $n$ with $\!\bmod n\!:\, a\,$ invertible $\Rightarrow a^{-1} \equiv a,\,$ i.e. $a^2\equiv 1$
72054
Show that $\deg f$ is even when $n$ is odd.
17047
Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
103784
Show that $n^2+11n+2$ is not divisible by $113^2$ ( n is integer)
47060
Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$