^2 => ^4
Source: Baltic Way 1992 #5
February 17, 2009
algebra proposedalgebra
Problem Statement
It is given that a^2\plus{}b^2\plus{}(a\plus{}b)^2\equal{}c^2\plus{}d^2\plus{}(c\plus{}d)^2. Prove that a^4\plus{}b^4\plus{}(a\plus{}b)^4\equal{}c^4\plus{}d^4\plus{}(c\plus{}d)^4.