MathForces: Math Olympiads
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Author: mathforces
Problem has been solved: 17 times

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The positive numbers $ a $, $b $ and $ c $ satisfy $\frac{b^3+3c^3}{a^2+a+1}=\frac{1-a}{2}$. Let $ x $ be the largest possible value of $ 2a + b + 3c $. It is known that $ y $ is the smallest positive integer for which $ x^y $ is an integer. What is $ x^y + y $ equal to?





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