This isn't homework, but an interest question I found on the web. I can't solve it though... Let [itex]p[/itex] be an odd prime. Determine all pairs [itex](m,n)[/itex] where m and n are positive integers and satisfy the below: [tex](p-1)(p^n+1)=4m(m+1)[/tex]. I have done by some simple inspection that m must be odd, but I'm not sure that helps. Does anyone know any theorems that may help?