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positive integer

Source: Ireland 2002

July 5, 2009
number theory unsolvednumber theory

Problem Statement

The sequence (an) (a_n) is defined by a_1\equal{}a_2\equal{}a_3\equal{}1 and a_{n\plus{}1}a_{n\minus{}2}\minus{}a_n a_{n\minus{}1}\equal{}2 for all n≥3. n \ge 3. Prove that an a_n is a positive integer for all n≥1 n \ge 1.
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