MathDB

1

Part of 1991 Austrian-Polish Competition

Problems(1)

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

Source: Austrian Polish 1991 APMC

5/1/2020
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.
CombinationsalgebraequationAustrian Polish