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2013 Silk Road
1
SRMC 2013 P1
SRMC 2013 P1
Source:
December 7, 2015
greatest common divisor
number theory
Problem Statement
Determine all pairs of positive integers
m
,
n
,
m, n,
m
,
n
,
satisfying the equality
(
2
m
+
1
;
2
n
+
1
)
=
2
(
m
;
n
)
+
1
(2^{m}+1;2^n+1)=2^{(m;n)}+1
(
2
m
+
1
;
2
n
+
1
)
=
2
(
m
;
n
)
+
1
, where
(
a
;
b
)
(a;b)
(
a
;
b
)
is the greatest common divisor
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