If $a, b$ and $n$ are natural numbers, then $a^{2 n-1}+b^{2 n-1}$ is divisible by

If $a, b$ and $n$ are natural numbers, then $a^{2 n-1}+b^{2 n-1}$ is divisible by
  1. $a+b$
  2. $a-b$
  3. $a^3+b^3$
  4. $a^2+b^2$

Solution

Here, we see that $(2 n-1)$ is an odd number $\therefore a^{2 n-1}+b^{2 n-1}$ is divisible by $a+b$.

Asked in: AP EAMCET 2011

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