Given that $p$ is a prime, and the sum of all positive divisors of $p^4$ is a perfect square, find the possible number of primes $p$ .
59091
A quartic diophantine equation
66216
Squares, Cubes and Prime numbers
144814
If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?
111967
Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.
78917
Show that for any prime numbers $p,q,r$, one has $p^2+q^2 \ne r^2$.
94019
Find all $p$'s such that $p^4 + p^3 + p^2 + p +1$ is a perfect square.
48691
Product of all prime numbers upto some prime $p$
18402
Sum of the reciprocals of divisors of a perfect number is $2$?
134121
Determining all the positive integers $n$ such that $n^4+n^3+n^2+n+1$ is a perfect square.
2264
Conjecture: the sequence of sums of all consecutive primes contains an infinite number of primes
72666
Prime Numbers And Perfect Squares
58182
How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
142584
Confusion in proof that primes $p = 4k + 1$ are uniquely the sums of two squares
127993
Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
75516
Relatively Prime Numbers and Number of Divisors of n
19588
$n!+1$ being a perfect square