MathDB
Problems
Contests
International Contests
Baltic Way
1996 Baltic Way
8
8
Part of
1996 Baltic Way
Problems
(1)
GCD of 1995 and 1996 term of the sequence - Baltic Way 1996
Source: 0
8/25/2007
Consider the sequence:
x
1
=
19
,
x
2
=
95
,
x
n
+
2
=
lcm
(
x
n
+
1
,
x
n
)
+
x
n
x_1=19,x_2=95,x_{n+2}=\text{lcm} (x_{n+1},x_n)+x_n
x
1
=
19
,
x
2
=
95
,
x
n
+
2
=
lcm
(
x
n
+
1
,
x
n
)
+
x
n
, for
n
>
1
n>1
n
>
1
, where
lcm
(
a
,
b
)
\text{lcm} (a,b)
lcm
(
a
,
b
)
means the least common multiple of
a
a
a
and
b
b
b
. Find the greatest common divisor of
x
1995
x_{1995}
x
1995
and
x
1996
x_{1996}
x
1996
.
number theory
greatest common divisor
least common multiple