I am Confused

Number Theory Level 4

Are there infinitely many positive integers $n$ that can not be expressed as $n=a^3+b^5+c^7+d^9+e^{11}$ , where $a,b,c,d$ and $e$ are positive integers?

No Yes

1 solution

Kay Xspre
Jan 28, 2016

An obvious example is when $n = m^3, m^5, m^7, m^9, m^{11}$ for prime number $m$ . By the result of Euclid's theorem (there are infinite prime numbers), n will be infinite and cannot be expressed as the sum given above without setting other values to zero, and zero is not a positive integer.

I am Confused

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