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3

Part of 2008 Switzerland - Final Round

Problems(1)

2^{5^{2^{5^{...}}}}+ 4^{5^{4^{5^{...}}}} divisible by 2008

Source: Switzerland - 2008 Swiss MO Final Round p3

12/26/2022
Show that each number is of the form 2525...+4545...2^{5^{2^{5^{...}}}}+ 4^{5^{4^{5^{...}}}} is divisible by 20082008, where the exponential towers can be any independent ones have height ≥3\ge 3.
number theorydividesdivisible