MathDB

2

Part of 2017 Azerbaijan EGMO TST

Problems(2)

Sequence

Source:

8/16/2016
Let (an)n≥0(a_n)_n\geq 0 and am+n+am−n=12(a2m+a2n)a_{m+n}+a_{m-n}=\frac{1}{2}(a_{2m}+a_{2n}) for every m≥n≥0.m\geq n\geq0. If a1=1,a_1=1, then find the value of a2007.a_{2007}.
algebraSequenceinduction
four numbers two deleted and replaced with a+b and ab

Source: Azerbaijan EGMO TST 2017, D2 P2

7/31/2023
Four numbers are written on the board: 1,3,6,10.1, 3, 6, 10. Each time two arbitrary numbers, aa and bb are deleted, and numbers a+ba + b and abab are written in their place. Is it possible to get numbers 2015,2016,2017,20182015, 2016, 2017, 2018 on the board after several such operations?
combinatorics