jasperE3 25.04.2021 19:16 Prove that if a,b,c are integers with $a+b+c=0$, then $2a^4+2b^4+2c^4$ is a perfect square.
natmath 25.04.2021 19:18 Substituting $c=-a-b$, we have $$2(a^4+b^4+(a+b)^4)$$$$=(a^2+b^2+(a+b)^2)^2$$
sqing 11.05.2021 08:09 jasperE3 wrote: Prove that if a,b,c are integers with $a+b+c=0$, then $2a^4+2b^4+2c^4$ is a perfect square. https://artofproblemsolving.com/community/c6h197840p1088181 https://artofproblemsolving.com/community/c4h2557219p21893760