Prove that (a^n + b^n) is always divisible by (a + b) if n is odd ?

• If n is odd, a^n + b^n = (a + b)(a^(n - 1) - a^(n - 2)*b + a^(n - 3)*b^2 -... + b^(n - 1)).
  Therefore, a^n + b^n is divisible by (a + b) when n is odd
• 11 years agoHelpfull: Yes(3) No(0)
• take N = 3
• 11 years agoHelpfull: Yes(0) No(1)
• n is odd means consider n value as 1,3,5,...
  -----> for n=1 (a^1+b^1) means a+b is divisible by a+b
  -----> for n=3 (a^3+b^3) means (a+b)(a^2-ab+b^2) is divisible by a+b
  Hence a^n+b^n is divisible by a+b..
• 11 years agoHelpfull: Yes(0) No(1)