MathDB

13

Part of 1985 ITAMO

Problems(1)

GCD of consecutive terms

Source:

3/14/2006
The numbers in the sequence 101, 104, 109, 116, …\dots are of the form an=100+n2a_n = 100 + n^2, where n=1n = 1, 2, 3, …\dots. For each nn, let dnd_n be the greatest common divisor of ana_n and an+1a_{n + 1}. Find the maximum value of dnd_n as nn ranges through the positive integers.
number theorygreatest common divisoralgorithmalgebrapolynomialEuclidean algorithm