# Yearly sequences

Define a sequence $$\displaystyle \{a_n\}_{n=1}^{n=2015}$$ which satisfies the following conditions:

$\bullet\quad \sum_{i=1}^{2015} a_{i}^{2} = 2015\\ \bullet\quad a_k\in \mathbb{Z} \setminus \{0\} \ \ \forall k\leq 2015~,k\in\mathbb{Z^+}$

How many such sequences are possible?

The answer is of the form $$a^b$$ where both $$a$$ and $$b$$ are non-negative integers and $$a$$ is a prime number. Find the value of $$(a+b)$$.

Clarification:

$\bullet\quad \sum_{i=1}^{n} a_i^2 = a_1^2+a_2^2+\ldots +a_{2015}^2 \ \textrm{is the sum of squares of the terms}$

Note: This problem is an extension of a very old problem from the Brilliant community whose link I cannot seem to find. I hope you all like it.

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