very easy.

Posts: 791
Joined: Aug 4, 2011

by hemangsarkar, Sep 9, 2012, 4:48 PM

Q) let $a,b,c,d$ be natural numbers such that $ab = cd$ .
prove that $a^n + b^n + c^n + d^n$ is a composite number.

my solution :

let $\frac{a}{c} = \frac{d}{b} = \beta$

so we have $a = \beta c$ and $d = \beta b$

putting these in $a^n + b^n + c^n + d^n$ , we get

$(\beta^n + 1)(c^n + b^n)$ whch is obviously composite.