# Not 1, not 2, not 3, not 4, but 5!

**Number Theory**Level 5

How many nonnegative integers \(n < 2014\) are there such that there will be no possible ordered quintuples of nonnegative integers (not necessarily distinct) \((a, b, c, d, e)\) that will satisfy the equation \(a^{12} + b^{10} + c^8 + d^6 + e^4 = 2^n - 1\)