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2018-IMOC
N3
N3
Part of
2018-IMOC
Problems
(1)
xy|(x^2-x+1)(y^2-y+1)
Source: IMOC 2018 N3
8/17/2021
Find all pairs of positive integers
(
x
,
y
)
(x,y)
(
x
,
y
)
so that
(
x
2
−
x
+
1
)
(
y
2
−
y
+
1
)
x
y
∈
N
.
\frac{(x^2-x+1)(y^2-y+1)}{xy}\in\mathbb N.
x
y
(
x
2
−
x
+
1
)
(
y
2
−
y
+
1
)
∈
N
.
number theory
Divisibility