Home Competitions Putnam 2013 A3
Suppose that the real numbers a 0 , a 1 , … , a n a_0, a_1, \dots, a_n a 0 , a 1 , … , a n x x x 0 < x < 1 0 < x < 1 0 < x < 1 a 0 1 − x + a 1 1 − x 2 + ⋯ + a n 1 − x n + 1 = 0. \frac{a_0}{1-x} + \frac{a_1}{1-x^2} + \cdots + \frac{a_n}{1 - x^{n+1}} = 0. 1 − x a 0 + 1 − x 2 a 1 + ⋯ + 1 − x n + 1 a n = 0. y y y 0 < y < 1 0 < y < 1 0 < y < 1 a 0 + a 1 y + ⋯ + a n y n = 0. a_0 + a_1 y + \cdots + a_n y^n = 0. a 0 + a 1 y + ⋯ + a n y n = 0.
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