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Expressing n as a^3+b^5+c^7+d^9+e^11

Source: Spanish Mathematical Olympiad 2013. Problem 4.

March 26, 2015
number theoryrepresentation

Problem Statement

Are there infinitely many positive integers nn that can not be represented as n=a3+b5+c7+d9+e11n = a^3+b^5+c^7+d^9+e^{11}, where a,b,c,d,ea,b,c,d,e are positive integers? Explain why.
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