# Not 1, not 2, not 3, not 4, but 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 $$a^{12} + b^{10} + c^8 + d^6 + e^4 = 2^n - 1$$

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