# Number theory at its best

Assume $$a,b$$ and $$c$$ are three positive integers that satisfy the conditions:

• $$a+b=c+12$$
• $$(a^2+b^2)^{1/3} =c+2$$
• $$c,b+4,2a+7$$ are in a geometric progression.

Find the value of $$a+b+c$$.

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