MathDB

3

Part of 2017 Federal Competition For Advanced Students, P2

Problems(1)

a_{n+1} = a_n + 2/a_n , sequence of rationals without square of rational

Source: 48th Austrian Mathematical Olympiad National Competition (Final Round, part 2) 24th May 2017 p3

5/25/2019
Let (an)n≥0(a_n)_{n\ge 0} be the sequence of rational numbers with a0=2016a_0 = 2016 and an+1=an+2ana_{n+1} = a_n + \frac{2}{a_n} for all n≥0n \ge 0. Show that the sequence does not contain a square of a rational number.
Proposed by Theresia Eisenkölbl
number theoryrationalrecurrence relationnumber theory with sequences