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Contests
National and Regional Contests
India Contests
Postal Coaching
2011 Postal Coaching
3
Find maximum and minimum value
Find maximum and minimum value
Source:
December 31, 2011
function
algebra unsolved
algebra
Problem Statement
Let
f
:
N
⟶
N
f : \mathbb{N} \longrightarrow \mathbb{N}
f
:
N
⟶
N
be a function such that
(
x
+
y
)
f
(
x
)
≤
x
2
+
f
(
x
y
)
+
110
(x + y)f (x) \le x^2 + f (xy) + 110
(
x
+
y
)
f
(
x
)
≤
x
2
+
f
(
x
y
)
+
110
, for all
x
,
y
x, y
x
,
y
in
N
\mathbb{N}
N
. Determine the minimum and maximum values of
f
(
23
)
+
f
(
2011
)
f (23) + f (2011)
f
(
23
)
+
f
(
2011
)
.
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