51. Find all triples of natural numbers such that the product of any two numbers in the triple, increased by 1, is divisible by twice the third number.
92.51. There is exactly one such triple - $(1,1,1)$. Hint. All three numbers in the triple - let's denote them $a, b$ and $c$ - must be pairwise coprime and odd. In this case, the expression $a b+b c+$ $+c a+1$ is divisible by each of the numbers $a, b$ and $c$, and therefore, it is divisible by their product.