MathDB

1

Part of 2012 Dutch Mathematical Olympiad

Problems(1)

(a-b)(a-c)(a-d)(b-c)(b-d)(c-d) is divisible by 12

Source: Dutch NMO 2012 p1

9/6/2019
Let a,b,ca, b, c, and dd be four distinct integers. Prove that (a−b)(a−c)(a−d)(b−c)(b−d)(c−d)(a-b)(a-c)(a-d)(b-c)(b-d)(c-d) is divisible by 1212.
divisiblenumber theory