IMO 1989 LL GBR27

Integers cm,n (m \geq0, n \geq0) are defined by cm,0 = 1 for all

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IMO 1989 LL GBR27

Origin: GBR

Problem

Integers cm,n (m \geq0, n \geq0) are defined by cm,0 = 1 for all m \geq0, c0,n = 1 for all n \geq0, and cm,n = cm−1,n −ncm−1,n−1 for all m > 0, n > 0. Prove that cm,n = cn,m for all m \geq0, n \geq0.