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Highest degree for 3-layer power tower (IMO ShortList 1991)

Source: IMO ShortList 1991, Problem 18 (BUL 1)

August 15, 2008
algebrabinomial theoremnumber theoryDivisibilityIMO Shortlist

Problem Statement

Find the highest degree k k of 1991 1991 for which 1991k 1991^k divides the number 1990^{1991^{1992}} \plus{} 1992^{1991^{1990}}.
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