8

Part of 2022 Thailand Mathematical Olympiad

Problems(1)

Another NT Sequence (Rational)

Source: 2022 Thailand MO Day 2 P8

Determine all possible values of

a_1

for which there exists a sequence

a_1, a_2, \dots

of rational numbers satisfying

a_{n+1}^2-a_{n+1}=a_n

for all positive integers

n

number theorySequence