Fermat's Little Theorem: Proving an integer exists which satisfies the following criteria mod $5$
33057
The inverse is a root of the reciprocal (reverse) polynomial.
60615
Product of $5$ consecutive integers cannot be perfect square
93820
Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
100336
Find an integer having the remainders $2,3,4,5$ when divided by $3,4,5,6$, respectively.
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
14783
A Number Theory problem (GCD)
119582
How to select the right modulus to prove that there do not exist integers $a$ and $b$ such that $a^2+b^2=1234567$?
8364
To show that Fermat number $F_{5}$ is divisible by $641$.
30136
Proof that a Combination is an integer
52530
There exists a prime congruent to $m$ mod $p$
78638
Find out all solutions of the congruence $x^2 \equiv29 \mod 5$.
124241
Finding all integers $k \geq 2$ such that $k^2 \equiv 5k \pmod{15}$. What is going on here?
49938
Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
41789
Fermat's theorem on sums of two squares
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
44182
Proving that an integer is even if and only if it is not odd
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5