Elementary Number Theory: If $p$ and $a$ are natural numbers with prime $p$, and $p^4|a^3$, then $p^2|a$.
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
36943
How to prove that $L=${$a^p$: p is prime} isn't regular?
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
89329
If a and b are relatively prime and ab is a square, then a and b are squares.
75318
How do you prove that a prime is the sum of two squares iff it is congruent to 1 mod 4?
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
34617
Number Theory: which primes are a sum of two squares?
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
78847
Bijection between Prime numbers and Natural numbers
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
146512
Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers
131141
Solutions to $p+1=2n^2$ and $p^2+1=2m^2$ in Natural numbers.
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
38748
There are infinitely many prime numbers $p$ for which $p + 2$ and $p + 4$ are also prime numbers