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Baltic Way
2001 Baltic Way
18
18
Part of
2001 Baltic Way
Problems
(1)
Relatively prime proof
Source:
1/3/2010
Let
a
a
a
be an odd integer. Prove that
a
2
m
+
2
2
m
a^{2^m}+2^{2^m}
a
2
m
+
2
2
m
and
a
2
n
+
2
2
n
a^{2^n}+2^{2^n}
a
2
n
+
2
2
n
are relatively prime for all positive integers
n
n
n
and
m
m
m
with
n
≠
m
n\not= m
n
=
m
.
modular arithmetic
number theory
relatively prime