How to prove $n=4k+3$ cannot be the sum of two squares, x and y are integers
46606
Can an integer of the form $4n+3$ written as a sum of two squares?
32985
Prove that there does not exist integer solutions for the diophantine equation $x^5 - y^2 = 4$.
345
Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.
81854
Prove $x^4 + 131 = 3y^4$ has no integer solutions
83862
How to prove that the number $1!+2!+3!+...+n!$ is never square?
131625
Expressing an integer as the sum of three squares
46102
Prove that $2^n +1$ in never a perfect cube
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
106716
The sum of square roots of non-perfect squares is never integer
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
156989
Proof that Hadamard matrices of order $4k+2$ don't exist
29799
Sum of four squares not a prime
147562
Sum of squares diophantine equation
30338
How to prove that $\sum_{k=0}^n \binom nk k^2=2^{n-2}(n^2+n)$
142724
Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
143113
Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$
5692
Proving that there is a perfect square between $n$ and $2n$