An algebra problem by Ankit Nigam

Algebra Level 5

Find the value of positive integer nn for which the quadratic equation k=1n(x+k1)(x+k)=10n\displaystyle \sum_{k = 1}^n(x + k - 1)(x + k) = 10n

has solutions α\alpha and α+1\alpha + 1 for some value of α\alpha.

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