MathDB

2

Part of 1994 Canada National Olympiad

Problems(1)

Decompose powers of (sqrt{2}-1)

Source: Canadian Mathematical Olympiad - 1994 - Problem 2.

5/13/2011
Prove that (2−1)n(\sqrt{2}-1)^n ∀n∈Z+\forall n\in \mathbb{Z}^{+} can be represented as m−m−1\sqrt{m}-\sqrt{m-1} for some m∈Z+m\in \mathbb{Z}^{+}.
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