Show that $35^{3} + 27^{3}$ is divisible by 62.

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Solution

Let $f (x) = x^{n} + y^{n}$
If $n$ is odd, $x^{n} + y^{n}$ is divisible by $(x + y)$
Here $35^{3} + 27^{3}$ is divisible by $62$

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