MathDB

1

Part of 2019 Federal Competition For Advanced Students, P1

Problems(1)

a_n = 14a_{n-1} + a_{n-2} , b_n = 6b_{n-1}-b_{n-2}, infinite common elements

Source: 2019 Austrian Federal Competition For Advanced Students, Part 1 p1

3/4/2020
We consider the two sequences (an)n≥0(a_n)_{n\ge 0} and (bn)n≥0(b_n) _{n\ge 0} of integers, which are given by a0=b0=2a_0 = b_0 = 2 and a1=b1=14a_1= b_1 = 14 and for n≥2n\ge 2 they are defined as an=14an−1+an−2a_n = 14a_{n-1} + a_{n-2} , bn=6bn−1−bn−2b_n = 6b_{n-1}-b_{n-2}. Determine whether there are infinite numbers that occur in both sequences
Sequencerecurrence relationRecurrencealgebraAustria