Prove that the only integer solution of the equation $a^2 + b^2 + c^2 = a^2 b^2$ is $a = b = c = 0$.
23835
Discrete mathematics - Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$.
147442
Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$
146294
Find all positive integers $a,b$ such that each of the equations $x^2-ax+b=0$ and $x^2-bx+a=0$ has distinct positive integral roots.
151153
Prove $\frac{a(a^2+2)}{3}$ is an integer for all integer $a\geqslant 1$
13914
If $a^2+b^2=c^2$ then $a$ or $b$ is even.
67666
show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
41689
Find all solutions: $x^2 + 2y^2 = z^2$
44309
Prove $5a^2 ≠ 3b^2$ for all non-zero rational numbers $a$ and $b$
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
27387
Show that $a+b+c=0$ implies that $32(a^4+b^4+c^4)$ is a perfect square.
17100
Prove that $\frac{b^2+c^2}{b+c}+\frac{c^2+a^2}{c+a}+\frac{a^2+b^2}{a+b} \ge a+b+c$
33469
Diophantine equation $ax + by = c$ has an integer solution $x_0, y_0$ if and only if $\gcd(a,b)|c$
85449
Show a,b,c congruences when $a^2+b^2=c^2$
111847
For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$
5729
If $a^2+b^2+c^2=1$ then prove the following.
33105
Find the value of $a^2-b^2+c^2$
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.