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2023 Israel National Olympiad
P2
P2
Part of
2023 Israel National Olympiad
Problems
(1)
Maximum solution to Diophantine equation
Source: 2023 Israel National Olympiad P2
12/16/2022
The non-negative integers
x
,
y
x,y
x
,
y
satisfy
x
+
x
+
60
=
y
\sqrt{x}+\sqrt{x+60}=\sqrt{y}
x
+
x
+
60
=
y
. Find the largest possible value for
x
x
x
.
number theory
Diophantine equation