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(\sqrt2+\sqrt3+\sqrt5)^1997 (IV Soros Olympiad 1997-98 Correspondence 10.7)

Source:

June 1, 2024

algebraRadicals

Problem Statement

Prove that the number

\left(\sqrt2+\sqrt3+\sqrt5\right)^{1997}

can be represented as

A\sqrt2+B\sqrt3+C\sqrt5+D\sqrt{30}

where

A

B

C

D

are integers. Find with approximation to

10^{-10}

the ratio

\frac{D}{A}