A Too Easy One in Fact!

Algebra Level 4

Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation \(x^2+x+1 = 0 \). If \(a,b\) and \(c\) are positive integers satisfying \(\gcd(a,b,c) = 22\) such that the quadratic equation \(ax^2+bx+ c=0 \) has \(\alpha^{62} \) and \(\beta^{62} \) as its roots, find the value of \(a+b+c\).

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