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Quadratic Sets

Author: mathforces
Problem has been solved: 9 times

Русский язык | English Language

Let us denote by $S(X)$ the sum of numbers in the set $X$. Let $a_n$ be the number of ways to split the set of numbers $2^0, 2^1, 2^2, \dots, 2^n$ into two non-empty sets $M$ and $F$ so that the equation $x^2- S(M)x + S(F)=0$ had an integer root. Find the sum $a_1 + a_2 + \dots + a_{2020}$.

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