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Mexico National Olympiad
1988 Mexico National Olympiad
5
5
Part of
1988 Mexico National Olympiad
Problems
(1)
gcd of a^2+b^2-nab and a+b divides n+2 , when a,b are coprime positive
Source: Mexican Mathematical Olympiad 1988 OMM P5
7/27/2018
If
a
a
a
and
b
b
b
are coprime positive integers and
n
n
n
an integer, prove that the greatest common divisor of
a
2
+
b
2
ā
n
a
b
a^2+b^2-nab
a
2
+
b
2
ā
nab
and
a
+
b
a+b
a
+
b
divides
n
+
2
n+2
n
+
2
.
number theory
coprime
greatest common divisor