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Determine all triples $(a,b,c)$ of positive integers such that each of the numbers $$ab-c, \quad bc-a, \quad ca-b$$ is a power of $2$.

(A power of $2$ is an integer of the form $2^n$, where $n$ is a non-negative integer.)

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So far I only figured out that if either two of $a,b,c$ is the same value, there are only 2 triples: $(2,2,2)$ and $(2,2,3)$.

But for $a\ne b\ne c\ne a$, I'm a bit lost as how to proceed. By trial and error there's a triple $(3,5,7)$ but how to get the complete triples?

Could someone pls gimme some hint?

athos
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1 Answers1

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With some trial and error, the only pairs with distinct digits seems to be (checked upto $(100,100,100)$):

(2,6,11)
(3,5,7)
RE60K
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