Proving that $2^{2a+1}+2^a+1$ is not a perfect square given $a\ge5$
15753
Solve the following equation in positive integers $x$ and $y$
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
28781
$k^{2}+(k+1)^{2}$ being a perfect square for infinitely many $k$
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
43048
When is $2^n \pm 1$ a perfect power
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
142513
Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square.
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
5927
How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
145558
Prove that $2^n+3^n $ is never a perfect square
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.
55077
prove that $2\sqrt5 +\sqrt{11}$ is irrational
136994
Proving :$\frac{1}{2ab^2+1}+\frac{1}{2bc^2+1}+\frac{1}{2ca^2+1}\ge1$
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime