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Austrian MO National Competition
2005 Federal Competition For Advanced Students, Part 1
2
a < 2005
a < 2005
Source: Austrian MO 2005 round 1
June 27, 2005
algebra unsolved
algebra
Problem Statement
For how many integers
a
a
a
with
∣
a
∣
≤
2005
|a| \leq 2005
∣
a
∣
≤
2005
, does the system
x
2
=
y
+
a
x^2=y+a
x
2
=
y
+
a
y
2
=
x
+
a
y^2=x+a
y
2
=
x
+
a
have integer solutions?
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