MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2009 Hanoi Open Mathematics Competitions
4
4
Part of
2009 Hanoi Open Mathematics Competitions
Problems
(1)
Prove that $a$ is divisible by 23
Source:
3/16/2014
Suppose that
a
=
2
b
a=2^b
a
=
2
b
, where
b
=
2
10
n
+
1
b=2^{10n+1}
b
=
2
10
n
+
1
. Prove that
a
a
a
is divisible by 23 for any positive integer
n
n
n
modular arithmetic
number theory open
number theory