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2023 USAJMO
1
Titu Factoring Troll
Titu Factoring Troll
Source: 2023 USAJMO Problem 1
March 23, 2023
USAJMO
Hi
Problem Statement
Find all triples of positive integers
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
that satisfy the equation
2
(
x
+
y
+
z
+
2
x
y
z
)
2
=
(
2
x
y
+
2
y
z
+
2
z
x
+
1
)
2
+
2023.
2(x+y+z+2xyz)^2=(2xy+2yz+2zx+1)^2+2023.
2
(
x
+
y
+
z
+
2
x
yz
)
2
=
(
2
x
y
+
2
yz
+
2
z
x
+
1
)
2
+
2023.
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