Find integers $a$ and $b$ such that $a^5b+3$ and $ab^5+3$ are both perfect cubes of integers?
69328
(USAJMO)Find the integer solutions:$ab^5+3=x^3,a^5b+3=y^3$
72389
Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
101708
Integers can be expressed as $a^3+b^3+c^3-3abc$
141173
Are there matrices such that $AB=I$ and $BA \neq I$
35326
There are infinitely many $N$ such that $\frac{N}{2}$ is a perfect square, $\frac{N}{3}$ is a perfect cube, and $\frac{N}{5}$ is a perfect fifth power
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
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
72591
Find a bijection to prove a fact about integer partitions
69874
Are there any integer solutions to $a^3=b^2$?
128107
find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
63774
If a and b are odd integers, then $8\mid (a^2-b^2)$
80229
How to prove this curiosity that has to do with cubes of certain numbers?
136964
Prove there exist 135 consecutive integers that each have a perfect cube $>1$ that divides it.
20834
Integer solutions to $c=a^2-b^2$
55100
The positive integer solutions for $2^a+3^b=5^c$
70619
Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.