How do you prove that $ n^5$ is congruent to $ n$ mod 10?
95141
$n^5-n$ is divisible by $10$?
52032
Prove that ${n^5 - n}$ is divisible by 5
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
23684
Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
82358
How to prove that $4^m + 5^m$ is divisible by 9 when m is an odd number
73020
Every integer is congruent to the sum of its digits mod 9
131241
primes congruent to 5 mod 6 and 1 mod p
127816
Number theory proof mod p
78638
Find out all solutions of the congruence $x^2 \equiv29 \mod 5$.
30172
Why is the order of $\mathbb{Z}[i]/\langle 3+i\rangle$ equal to 10?
61825
Congruence class $[a]$ modulo $m$, $\gcd(x, m) = \gcd(a, m)$
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
112541
Prove that $n^2 + 2^n$ is composite if $n\not\equiv3\pmod{6}$.
48875
$n^3 \equiv n^5 \pmod{12} $?
59475
Show that $\sqrt{n+1}-\sqrt{n}\to0$