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Romania District Olympiad 2010

Source: Grade IX

March 13, 2010
algebra proposedalgebra

Problem Statement

Consider the sequence (xn)n≥0 (x_n)_{n\ge 0} where x_n\equal{}2^{n}\minus{}1\ ,\ n\in \mathbb{N}. Determine all the natural numbers p p for which: s_p\equal{}x_0\plus{}x_1\plus{}x_2\plus{}...\plus{}x_p is a power with natural exponent of 2 2.
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