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Wiz14
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For each integer n > 1, let p(n) denote the largest prime factor of n. Determine all
triples (x; y; z) of distinct positive integers satisfying
x; y; z are in arithmetic progression,
p(xyz) <= 3.
So far I have come up with 22k + 1, 22k + 1 + 22k, and 22k + 2 other than the solutions 1,2,3, or 2,3,4 or 6,9,12. Is this sufficient?
triples (x; y; z) of distinct positive integers satisfying
x; y; z are in arithmetic progression,
p(xyz) <= 3.
So far I have come up with 22k + 1, 22k + 1 + 22k, and 22k + 2 other than the solutions 1,2,3, or 2,3,4 or 6,9,12. Is this sufficient?