MathDB
Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2010 Korea Junior Math Olympiad
6
6
Part of
2010 Korea Junior Math Olympiad
Problems
(1)
Prove that the number is compound
Source: KJMO 2010 Problem 6
9/6/2018
Let
n
∈
N
n\in\mathbb{N}
n
∈
N
and
p
p
p
is the odd prime number. Define the sequence
a
n
a_n
a
n
such that
a
1
=
p
n
+
1
a_1=pn+1
a
1
=
p
n
+
1
and
a
k
+
1
=
n
a
k
+
1
a_{k+1}=na_k+1
a
k
+
1
=
n
a
k
+
1
for all
k
∈
N
k \in \mathbb{N}
k
∈
N
. Prove that
a
p
−
1
a_{p-1}
a
p
−
1
is compound number.
number theory