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Each term of sequence differs by 2 from an integral square

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January 3, 2011
calculusintegrationnumber theory unsolvednumber theory

Problem Statement

A sequence {un}\{ u_n \} of integers is defined by u1=2,u2=u3=7,u_1 = 2, u_2 = u_3 = 7, un+1=unun−1−un−2, for n≥3u_{n+1} = u_nu_{n-1} - u_{n-2}, \text{ for }n \geq 3 Prove that for each n≥1n \geq 1, unu_n differs by 22 from an integral square.
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