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IMO Shortlist
2014 IMO Shortlist
N2
IMO Shortlist 2014 N2
IMO Shortlist 2014 N2
Source:
July 11, 2015
IMO Shortlist
number theory
equation
IMO Shortlist 2014
Problem Statement
Determine all pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
of positive integers such that
7
x
2
−
13
x
y
+
7
y
2
3
=
∣
x
−
y
∣
+
1.
\sqrt[3]{7x^2-13xy+7y^2}=|x-y|+1.
3
7
x
2
−
13
x
y
+
7
y
2
=
∣
x
−
y
∣
+
1.
Proposed by Titu Andreescu, USA
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