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Baltic Way
2014 Baltic Way
19
19
Part of
2014 Baltic Way
Problems
(1)
Possible values of gcd
Source: Baltic Way 2014, Problem 19
11/11/2014
Let
m
m
m
and
n
n
n
be relatively prime positive integers. Determine all possible values of
gcd
(
2
m
−
2
n
,
2
m
2
+
m
n
+
n
2
−
1
)
.
\gcd(2^m - 2^n, 2^{m^2+mn+n^2}- 1).
g
cd
(
2
m
−
2
n
,
2
m
2
+
mn
+
n
2
−
1
)
.
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