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National and Regional Contests
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MAA AMC
USAJMO
2024 USAJMO
5
average FE
average FE
Source: USAJMO 2024/5
March 21, 2024
USA(J)MO
USAJMO
function
functional equation
PointWise Trap
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
that satisfy
f
(
x
2
−
y
)
+
2
y
f
(
x
)
=
f
(
f
(
x
)
)
+
f
(
y
)
f(x^2-y)+2yf(x)=f(f(x))+f(y)
f
(
x
2
−
y
)
+
2
y
f
(
x
)
=
f
(
f
(
x
))
+
f
(
y
)
for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.Proposed by Carl Schildkraut
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