MathDB
There is a term of the sequence <sqrt{m}

Source: Serbia NMO 2010 problem 6

March 11, 2011
number theory unsolvednumber theory

Problem Statement

Let a0a_0 and ana_n be different divisors of a natural number mm, and a0,a1,…,ana_0, a_1, \ldots, a_n be a sequence of natural numbers such that it satisfies ai+1=∣ai±ai−1∣ for 0<i<na_{i+1} = |a_i\pm a_{i-1}|\text{ for }0 < i < n If gcd(a0,a1,…,an)=1gcd(a_0,a_1,\ldots, a_n) = 1, show that there exists a term of the sequence that is smaller than m\sqrt{m} .
Proposed by Dusan Djukic
Back to ProblemsView on AoPS