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Part of 1984 IMO Longlists

Problems(1)

Prove that all terms of number triangle are integers

Source:

10/12/2010
A “number triangle” (tn,k)(0≤k≤n)(t_{n, k}) (0 \le k \le n) is defined by tn,0=tn,n=1(n≥0),t_{n,0} = t_{n,n} = 1 (n \ge 0), t_{n+1,m} =(2 -\sqrt{3})^mt_{n,m} +(2 +\sqrt{3})^{n-m+1}t_{n,m-1}   (1 \le m \le n) Prove that all tn,mt_{n,m} are integers.
number theory unsolvednumber theory