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China Northern Mathematical Olympiad 2014 , Problem 3
Source: China Sijiazhuang , Aug 2014
8/12/2014
Determine whether there exist an infinite number of positive integers
x
,
y
x,y
x
,
y
satisfying the condition:
x
2
+
y
∣
x
+
y
2
.
x^2+y \mid x+y^2.
x
2
+
y
∣
x
+
y
2
.
Please prove it.
Diophantine equation
number theory proposed
number theory