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Archive for April 8th, 2009

A23 Prove that if

1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}

is expressed as a fraction, where p>3 is a prime, then p^2 divides the numerator.

A24 Let p>3 be a prime number and k=\lfloor\frac{2p}{3}\rfloor. Prove that

{p \choose 1}+{p \choose 2}+\cdots+{p \choose k}

is divisible by p^2.

Here is the official solution file: pen18.pdf

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