# FindInstance confused by CoprimeQ

For some reason when I type

FindInstance[a + b == c && CoprimeQ[a, b, c] == True, {a, b, c}, Integers]


Mathematica just immediately returns my input as its output, even though the very simple solution {1,2,3} should suffice. Why doesn't it even attempt to solve for this, and how can I fix it?

As with most *Q functions, CoprimeQ will evaluate to True or False immediately:

CoprimeQ[a,b,c]


False

You could instead use GCD:

FindInstance[
a + b == c && And @@ Thread[GCD @@@ Subsets[{a, b, c}, {2}] == 1],
{a, b, c},
Integers
]


{{a -> 1, b -> 0, c -> 1}}

although this approach won't work to find your example.