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2024 Nepal TST
P2
P2
Part of
2024 Nepal TST
Problems
(1)
Function can't not satisfy this!
Source: 2024 Nepal TST P2
4/12/2024
Let
f
:
N
→
N
f: \mathbb{N} \to \mathbb{N}
f
:
N
→
N
be an arbitrary function. Prove that there exist two positive integers
x
x
x
and
y
y
y
which satisfy
f
(
x
+
y
)
≤
f
(
2
x
+
f
(
y
)
)
f(x+y) \le f(2x+f(y))
f
(
x
+
y
)
≤
f
(
2
x
+
f
(
y
))
.(Proposed by David Anghel, Romania)
function
Natural Numbers
inequalities