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Part of PEN A Problems

Problems(1)

Source:

(Wolstenholme's Theorem) Prove that if

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

is expressed as a fraction, where

p \ge 5

is a prime, then

p^{2}

divides the numerator.

quadraticsGaussmodular arithmeticnumber theoryrelatively primeDivisibility Theorypen