Prove that there are no integers $x$ and $y$ such that $ (x/y)^2 = 2$
91101
Proving $\sqrt2$ is irrational
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
152638
The set of integers $n$ expressible as $n=x^2+xy+y^2$
70522
$y^2 = \frac{x^5 - 1}{x-1}$ & $x,y \in \mathbb{Z}$
27911
How can I prove that $xy\leq x^2+y^2$?
113359
Proving that $x^2 + 4$ is not divisible by $3$
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
94700
Integer solutions for $x^3+2=y^2$?
25784
Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$.
77763
Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
68807
How to show that the ring $S/A$ has no zero divisors? (Hungerford, Algebra, Problem 12, Chapter III, Section 2)
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
99000
No polynomial with integer coefficients satisfies the conditions
5595
$x^y = y^x$ for integers $x$ and $y$
144863
Finding integer solutions to $y^2=x^3-2$
20593
Show that if $a \neq b$ and a and b are positive then $\frac{a}{b}+\frac{b}{a}$ is never an integer
32985
Prove that there does not exist integer solutions for the diophantine equation $x^5 - y^2 = 4$.