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6

Part of 1995 Portugal MO

Problems(1)

x is rational iff x, x+1, ..., x+n, .. contains at least 3 terms in geom. progr

Source: Portugal OPM 1995 p6

5/18/2024
Prove that a real number xx is rational if and only if the sequence x,x+1,x+2,x+3,...,x+n,...x, x+1, x+2, x+3, ..., x+n, ... contains, at least least three terms in geometric progression.
rationalalgebrageometric progression