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(a,b,c,d) of positive integers with 0<a,b,c,d <p-1 satisfy ad = bc mod p

Source: Mexican Mathematical Olympiad 1992 OMM P2

July 29, 2018
number theoryprime

Problem Statement

Given a prime number pp, how many 44-tuples (a,b,c,d)(a, b, c, d) of positive integers with 0≤a,b,c,d≤p−10 \le a, b, c, d \le p-1 satisfy ad=bcad = bc mod pp?
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