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Number theory with series

Source: Moldova TST 2020

March 7, 2020
progressionsArithmetic Progressiongeometric progressionnumber theory

Problem Statement

All members of geometrical progression (bn)n≥1(b_n)_{n\geq1} are members of some arithmetical progression. It is known that b1b_1 is an integer. Prove that all members of this geometrical progression are integers. (progression is infinite)
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