Proving that $n^5 \equiv n\mod 30$
3611
How to prove $n^5 - n$ is divisible by $30$ without reduction
21108
Perfect squares and modularly congruency in mod 5
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
30630
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
144802
Prove no solution to $x^2\equiv3\bmod5$
124241
Finding all integers $k \geq 2$ such that $k^2 \equiv 5k \pmod{15}$. What is going on here?
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
56464
Proving the irrationality of $e^n$
77383
Prove that $n^3=n \text{ mod }6$ for every integer $n$.
55060
Prove that $n^2+n+41$ is prime for $n<40$
133819
How to prove that $364 \mid n^{91} - n^7$?
112541
Prove that $n^2 + 2^n$ is composite if $n\not\equiv3\pmod{6}$.
136279
Infinitely many primes $\equiv 3 \mod 4$
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers