Hi evebody,

Is there any proof of:

Let $P_1, P_2$ two different primes

Prove (or plz give me a link) that if

$
a=P_1^s-P_2^s
$

then

$
$

$
$

For every positive integer s

(/= means not equal)

Thank you a lot

2. $a\equiv-p_2^s\,(\bmod\,p_1)\not\equiv0\,(\bmod\,p_1)$ as $p_1$ does not divide $p_2.$

Similarly $a\equiv p_1^s\,(\bmod\,p_2)\not\equiv0\,(\bmod\,p_2)$ as $p_2$ does not divide $p_1.$

3. Indeed...
I missed the spot that

$