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Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

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Powerful Factors

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Use the fact that:

$x^2-y^2$ = $(x-y)(x+y)$
$x^3+y^3$ = $(x+y)(x^2-xy+y^2)$

to find the highest power of $2$ and the highest power of $3$ which divide $5^{36}-1$.