Japanese | Can you solve this ? | Math Olympiad | Calculators NOT allowed 

a,b,-a-b ... t^3 - ( a^2 +ab+b^2)t +ab(a+b) = 0 t^4- (a^2+ab+b^2)t^2 +ab(a+b)t = 0 a^n + b^n + (-a-b)^n = f(n) f(4) - (a^2+ab+b^2)f(2) + ab(a+b) f(1) = 0 f(4) = 2(a^2 + ab + b^2)^2

Why does EVERYONE rewrite the effing problem just below the problem?

Superb