Floor of prime powers

For students of class 11-12 (age 16+)
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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.

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Re: Floor of prime powers

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

- 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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