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Olympiad Sequences and Series

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Problems 1

Can we find a sequence of reals ai≠0a_i\neq0ai=0 such that each polynomial pn(x)=a0+a1x+⋯+anxnp_n(x) = a_0 + a_1 x + \dots + a_n x^npn(x)=a0+a1x+⋯+anxn has all its roots r…