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Korea Junior Mathematics Olympiad
2023 Korea Junior Math Olympiad
6
Integer inequality
Integer inequality
Source: KJMO 2023 P6
November 4, 2023
inequalities
Problem Statement
Find the maximum value of real number
A
A
A
such that
3
x
2
+
y
2
+
1
≥
A
(
x
2
+
x
y
+
x
)
3x^2 + y^2 + 1 \geq A(x^2 + xy + x)
3
x
2
+
y
2
+
1
≥
A
(
x
2
+
x
y
+
x
)
for all positive integers
x
,
y
.
x, y.
x
,
y
.
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