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Arithmetic sequence

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January 29, 2016
arithmetic sequencenumber theory

Problem Statement

ana_n sequence is a arithmetic sequence with all terms be positive integers. (for ana_n non-constant sequence) Let pnp_n is greatest prime divisor of ana_n. Prove that (anpn)(\frac{a_n}{p_n}) sequence is infinity.
Note: If we find a M>0M>0 constant such that xn≤Mx_n \leq M for all n∈Nn \in {\mathbb N}'s, (xn)(x_n) sequence is non-infinite, but we can't find MM, (xn)(x_n) sequence is infinity
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