MathDB
TST-Romania, 2002

Source: sequence of integers

October 9, 2009
algebrapolynomialinductionDiophantine equationnumber theory proposednumber theory

Problem Statement

The sequence (an) (a_n) is defined by: a_0\equal{}a_1\equal{}1 and a_{n\plus{}1}\equal{}14a_n\minus{}a_{n\minus{}1} for all n≥1 n\ge 1. Prove that 2a_n\minus{}1 is a perfect square for any n≥0 n\ge 0.
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