How do you prove that $ n^5$ is congruent to $ n$ mod 10?
73307
Why is the last digit of $n^5$ equal to the last digit of $n$?
9787
Primitive roots modulo primes congruent to n!
38285
What is $(65!)^2$ congruent to mod $131$?
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
85106
Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems
6918
Primes congruent to 1 mod 6
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
105225
Number Theory: Complete set of residues modulo $n$
55266
Prove that $(n+1)^{n-1}<n^n$
131241
primes congruent to 5 mod 6 and 1 mod p
34192
Solve $x^{5} \equiv 2$ mod $221\ $ [Taking modular $k$'th roots if unique]
105442
Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$
103545
Prove "casting out nines" of an integer is equivalent to that integer modulo 9
78638
Find out all solutions of the congruence $x^2 \equiv29 \mod 5$.
77240
Show that $4 + \sqrt{10}$ is not prime in $\mathbb{Z}\bigl [\sqrt{10}\bigr]$
59475
Show that $\sqrt{n+1}-\sqrt{n}\to0$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.