# Product of Even Numbers

Number Theory Level pending

What is the largest integer $$N\leq2017$$ such that there is exactly one way to express $$N$$ as a product of even positive integers $$p$$ and $$q$$ with

• None of $$p$$ and $$q$$ is divisible by $$4$$ and

• $$p\leq q$$.

Hint:

• For $$N=12$$, there is exactly one way; namely, $$12=2\times 6$$.
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