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1/3+ 2/4+... +(p -3)/(p - 1)=a/b , p prime >=b, prove p /a

Source: Norwegian Mathematical Olympiad 2013 - Abel Competition p3

September 4, 2019
number theoryprimedivides

Problem Statement

A prime number p≥5p \ge 5 is given. Write 13+24+...+p−3p−1=ab\frac13+\frac24+... +\frac{p -3}{p - 1}=\frac{a}{b} for natural numbers aa and bb. Show that pp divides aa.
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