# Expressing Integers As A Difference Of Squares

Let $$f(n)$$ be defined as the number of ways a positive integer $$n$$ can be expressed as $$a^2-b^2$$, where $$a$$ and $$b$$ are positive integers.

Let $$g(n)$$ be defined as the smallest possible positive integer $$y$$ such that $$f(y)=n$$.

If $$M$$ is the least common multiple of $$g(1)$$, $$g(2)$$, $$g(3)$$, $$g(4)$$, and $$g(5)$$, then what is $$f(M)$$?

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