MathDB
Problems
Contests
Undergraduate contests
Putnam
1997 Putnam
5
Putnam 1997 B5
Putnam 1997 B5
Source:
May 30, 2014
Putnam
modular arithmetic
college contests
Problem Statement
Let us define a sequence
{
a
n
}
n
≥
1
\{a_n\}_{n\ge 1}
{
a
n
}
n
≥
1
. Define as follows:
a
1
=
2
and
a
n
+
1
=
2
a
n
for
n
≥
1
a_1=2\text{ and }a_{n+1}=2^{a_n}\text{ for }n\ge 1
a
1
=
2
and
a
n
+
1
=
2
a
n
for
n
≥
1
Show this :
a
n
≡
a
n
−
1
(
m
o
d
n
)
a_{n}\equiv a_{n-1}\pmod n
a
n
≡
a
n
−
1
(
mod
n
)
Back to Problems
View on AoPS