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a,b, and c are positive integers.
b/a is an integer, say m, or b = am.
a, b and c are in GP. So b^2 = ac, or
a^2*m^2 = ac, or
c = am^2 …(1)
(a+b+c)=3(b+2), or
a-2b+c = 6, or
a -2am +am^2 = 6, or
a[m^2–2m+1]=6
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