Floor of prime powers

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mutasimmim
Posts: 107
Joined: Sun Dec 12, 2010 10:46 am

Floor of prime powers

Unread post by mutasimmim » Fri Sep 12, 2014 10:20 pm

Let $p,q$ be two distinct odd primes. Prove that $ \lfloor \frac {p^q+q^p}{pq} \rfloor$ is always even. Here $\lfloor \rfloor$ denotes the floor function.

Nirjhor
Posts: 136
Joined: Thu Aug 29, 2013 11:21 pm
Location: Varies.

Re: Floor of prime powers

Unread post by Nirjhor » Fri Sep 12, 2014 11:47 pm

FLT
- What is the value of the contour integral around Western Europe?

- Zero.

- Why?

- Because all the poles are in Eastern Europe.


Revive the IMO marathon.

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