MathDB

Problem 2

Part of 2020 Brazil Undergrad MO

Problems(1)

(Not) Almost Fibonacci

Source: Brazilian Undergrad MO 2020 Problem 2

5/17/2022
For a positive integer aa, define F1(a)=1F_1 ^{(a)}=1, F2(a)=aF_2 ^{(a)}=a and for n>2n>2, Fn(a)=Fn−1(a)+Fn−2(a)F_n ^{(a)}=F_{n-1} ^{(a)}+F_{n-2} ^{(a)}. A positive integer is fibonatic when it is equal to Fn(a)F_n ^{(a)} for a positive integer aa and n>3n>3. Prove that there are infintely many not fibonatic integers.
Brazilian Undergrad MO 2020number theorySequencesBrazilian Undergrad MO