Y by
Find all pairs
of positive integers, for which
![$$(a, b) + 3[a, b] = a^3 - b^3$$](//latex.artofproblemsolving.com/b/8/3/b83f52a0152dc39b6d966880a1d6ca824a0f3786.png)
Here
denotes the greatest common divisor of
, and
denotes the least common multiple of
.
Proposed by Oleksiy Masalitin

![$$(a, b) + 3[a, b] = a^3 - b^3$$](http://latex.artofproblemsolving.com/b/8/3/b83f52a0152dc39b6d966880a1d6ca824a0f3786.png)
Here


![$[a, b]$](http://latex.artofproblemsolving.com/d/a/2/da2e551d2ca2155b8d8f4935d2e9757722c9bab6.png)

Proposed by Oleksiy Masalitin
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