If a , b and n are natural numbers, then a 2 n − 1 + b 2 n − 1 is divisible by

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

MathematicsBasic of MathematicsAP EAMCETAP EAMCET 2011

Options:

A $a+b$
B $a-b$
C $a^3+b^3$
D $a^2+b^2$

Solution:

2817 Upvotes Verified Answer

The correct answer is: $a+b$

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

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