Show that it doesn't exist any of natural number $ n = 4m + 3$ that $ n= x^2+y^2 $ for any natural x and y
110195
$p=4n+3$ never has a Decomposition into $2$ Squares, right?
21906
Show $3^m + 3^n +1$ cannot be a perfect square for $m,n$ being positive integers.
4946
Non-existence of irrational numbers?
84379
Prove that there is no integer a for which $a^2 - 3a - 19$ is divisible by 289
134834
$n^2 + (n+1)^2 = m^3$ has no solution in the positive integers
156940
There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$
83542
A natural problem in $\textrm{S}_2^\textrm{P}$?
90329
Prove there is no simple group of order $729$
48051
Proof related to natural numbers
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
33705
Is $0$ a natural number?
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.
149716
Prove that $ \sqrt{n(n+1)(n+2)(n+3)+1} $ is always a natural number
113695
Show that there is no integer n with $\phi(n)$ = 14
129697
Prove that a limit doesn't exist
69902
$3$ never divides $n^2+1$
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.