sqrt2, sqrt5 and sqrt7 cannot be terms of the same geometric progression.
This is an interesting number theory problem using the parity and the properties of geometric progressions. Source: Problem 205, K¨oz´episkolai Matematikai ´es Fizikai Lapok Vol. III, No. 3 (1926), p. 92, http://db.komal.hu/scan/ http://db.komal.hu/scan/1926/11/92611... (in Hungarian).
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