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(m \choose 2) = 3 (n \choose 4) combinations

Source: Austrian Polish 1991 APMC

May 1, 2020
CombinationsalgebraequationAustrian Polish

Problem Statement

Show that there are infinitely many integers m≥2m \ge 2 such that (m2)m \choose 2 =3= 3 (n4)n \choose 4 holds for some integer n≥4n \ge 4. Give the general form of all such mm.
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