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Existence of integers

Source:

December 31, 2011
algebrapolynomialalgebra unsolved

Problem Statement

Prove that there exist integers a,b,ca, b, c all greater than 20112011 such that (a+b)c=…2010⋅2011…(a+\sqrt{b})^c=\ldots 2010 \cdot 2011\ldots [Decimal point separates an integer ending in 20102010 and a decimal part beginning with 20112011.]
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