Show that, there are no integers $(m, n)$ such that, $m^2 + (m + 1)^2 = n^4 + (n + 1)^4$ .
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
27494
$P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$
108244
Proof without solving equation that if $(1+z)^n = (1-z)^n$ then Re(z) = 0. Did I do it right?
28274
Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
36862
A question about proving that there is no greatest common divisor
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.
68068
For any integer n greater than 1, $4^n+n^4$ is never a prime number.
24322
Prove that the equation $18x+42y=22$ has no integer solution?
32771
The equation $X^{n} + Y^{n} = Z^{n}$ , where $ n \geq 3$ is a natural number, has no solutions at all where $X,Y,Z$ are intergers.
99037
Prove the sum of all numbers that do not have a multiplicative inverse mod $n$
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
10606
Finding how multiplication and addition behave on $\mathbb{F}_4$ without any result
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.