Is there any four positive integer for which $a^2 + b^2 = c^2 + d^2$?
33633
Re:$ (a,b,c,d)=(pr+qs, qr-ps,pr-qs,ps+qr) $
55100
The positive integer solutions for $2^a+3^b=5^c$
126820
How many positive integer solutions are there to the equality $x_1+x_2+...+x_r= n$?
132098
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
5729
If $a^2+b^2+c^2=1$ then prove the following.
20486
Numbers representable as $x^2 + 2y^2$
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
61022
Diophantine Equations : Solving $a^2+ b^2=2c^2$
18530
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
4885
Polynomials with integer coefficients such that $p(a)=b,p(b)=c,p(c)=a$
97750
Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$.
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
146439
Is every sufficiently large positive integer of the form $ab + ac + bc + 1$?
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
85449
Show a,b,c congruences when $a^2+b^2=c^2$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
34275
How do I show that $\frac {a^2}b + \frac {b^2}c + \frac {c^2}d + \frac {d^2}a \ge 4$ for $a^2 + b^2 + c^2 + d^2 = 4$?