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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