MathDB

10

Part of 2006 QEDMO 3rd

Problems(1)

a_{n+1}=(a_{n}^{2}+a_{n-1}^{2})/ a_{n-2} sequence of integer terms

Source: 3rd QEDMO 2006 p10

11/9/2020
Define a sequence (an)n∈N\left( a_{n}\right) _{n\in\mathbb{N}} by a1=a2=a3=1a_{1}=a_{2}=a_{3}=1 and an+1=an2+an−12an−2a_{n+1}=\dfrac{a_{n}^{2}+a_{n-1}^{2}}{a_{n-2}} for every integer n≥3n\geq3. Show that all elements aia_{i} of this sequence are integers.
(L. J. Mordell and apparently Dana Scott, see also http://oeis.org/A064098)
Sequencenumber theory with sequencesRecurrencenumber theory