Question 1

Let $$N$$ be the set of all positive integers and $$S = \left\{(a,b,c,d) \in N^{4} : a^{2} + b^{2} + c^{2} = d^{2}\right\}$$. Find the largest positive integer $$m$$ such that $$m$$ divides abcd for all $$(a, b, c, d) \in S$$.

Correct Answer: e

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