Question 34
Prove that the ratio
$$
\frac{1^1 + 3^3 + 5^5 + \dots + (2^{2012} - 1)^{(2^{2012} - 1)}}{2^{2012}}
$$
is an odd integer.
$$
\frac{1^1 + 3^3 + 5^5 + \dots + (2^{2012} - 1)^{(2^{2012} - 1)}}{2^{2012}}
$$
is an odd integer.
MathNet 2013 Question 34
Math Olympiad Vault · MathNet 2013