Q43 / 160 · TS EAMCET 2018 (04 May Shift 2) · Mathematics

$x^n+y^n$ is divisible by

  • A
    $x-y$ for all $n \in N$
  • B
    $x+y$ for all $n \in N$
  • Correct answer
    C
    $x+y$ for all $n=2 m-1, m \in N$
  • D
    $x+y$ for all $n=2 m, m \in N$

Solution

Given, $x^n+y^n$ At $n=1, x+y$, which is divisible by $x+y$. $n=2, x^2+y^2$, which is not divisible by $x+y$. $n=3, x^3+y^3$, which is divisible by $x+y$. Hence, clearly $x^n+y^n$ is divisible by $n=$ odd numbers as $n=2 m-1$, where $M \in N$.

Hence, the correct answer is option: 'C'.

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