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Determine with proof all triples (a, b, ...

Determine with proof all triples (a, b, c) of positive integers satisfying `1/a+2/b+3/c=1` where a is a prime number and `a le b le c`

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The correct Answer is:
(2,5,30)(2,6,18)(2,7,14)(2,8,12)(2,10,10)(3,4,6)(3,6,9)
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