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European Mathematical Cup
2018 European Mathematical Cup
2
Find all pairs (x; y)
Find all pairs (x; y)
Source: 7th European Mathematical Cup , Junior Category, Q2
December 25, 2018
number theory
Problem Statement
Find all pairs
(
x
;
y
)
(x; y)
(
x
;
y
)
of positive integers such that
x
y
∣
x
2
+
2
y
−
1.
xy | x^2 + 2y -1.
x
y
∣
x
2
+
2
y
−
1.
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