TargetIIT

n to the power p -n;divisible by p. p is a prime number. prove it

for those who have`nt followed, the question is this:  


[b][im]http://codecogs.izyba.com/gif.latex?n%5E%7Bp-n%7D[/im] is divisible by [im]http://codecogs.izyba.com/gif.latex?p[/im].  then prove that p is a prime  number...[/b]      

now try it.


[hide]Here `n`  must be a integer  as far  as my solution is concerned..
[/hide]

let's take an ex:- 3[p]5-3[/p] is not divisible by 5.but that doesen't mean 5 is not a prime no.

He's asking for Fermat's theorem, proof by Induction