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Problems
Contests
National and Regional Contests
Korea Contests
Korea National Olympiad
2005 Korea National Olympiad
1
1
Part of
2005 Korea National Olympiad
Problems
(1)
19th kmo #1
Source: KMO round 2, problem 1
2/3/2006
For two positive integers a and b, which are relatively prime, find all integer that can be the great common divisor of
a
+
b
a+b
a
+
b
and
a
2005
+
b
2005
a
+
b
\frac{a^{2005}+b^{2005}}{a+b}
a
+
b
a
2005
+
b
2005
.
algorithm
number theory
greatest common divisor
relatively prime
Euclidean algorithm
number theory unsolved