Integers satisfying $a^b=b^a$
5595
$x^y = y^x$ for integers $x$ and $y$
71012
If $a, b$ are positive integers such that $a|b^2, b^2|a^3,....$ then $a=b$.
73079
Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$
94700
Integer solutions for $x^3+2=y^2$?
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
87267
Conjecture similar to Fermat's Theorem.
77547
Find integers $a,b,c,d$ such that
134857
Find $(a,b)$ if $x^2-bx+a = 0, x^2-ax+b = 0$ both have distinct positive integers roots
114185
Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
103274
Integer solutions to the equation $a^3+b^3+c^3=30$
107990
Does there exist an integer $x$ satisfying the following congruences?
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
33593
An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$
54430
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$
135750
Prove that if a and b are integers, then there are unique integers q and r such that $a = bq + r$, $-|b|/2 < r \le |b|/2$
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.