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Czech and Slovak Olympiad III A
2008 Czech and Slovak Olympiad III A
3
czech republic,czech and slovakia MO(third round),2008 p3
czech republic,czech and slovakia MO(third round),2008 p3
Source:
February 25, 2012
number theory
greatest common divisor
number theory proposed
Problem Statement
Find all pairs of integers
(
a
,
b
)
(a,b)
(
a
,
b
)
such that
a
2
+
a
b
+
1
∣
b
2
+
a
b
+
a
+
b
−
1
a^2+ab+1\mid b^2+ab+a+b-1
a
2
+
ab
+
1
∣
b
2
+
ab
+
a
+
b
−
1
.
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