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GCD of 1995 and 1996 term of the sequence - Baltic Way 1996

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August 25, 2007

number theorygreatest common divisorleast common multiple

Problem Statement

Consider the sequence:

x_1=19,x_2=95,x_{n+2}=\text{lcm} (x_{n+1},x_n)+x_n

, for

n>1

, where

\text{lcm} (a,b)

means the least common multiple of

a

and

b

. Find the greatest common divisor of

x_{1995}

and

x_{1996}