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Putnam
1963 Putnam
B3
B3
Part of
1963 Putnam
Problems
(1)
Putnam 1963 B3
Source: Putnam 1963
5/1/2022
Find every twice-differentiable function
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
that satisfies the functional equation
f
(
x
)
2
−
f
(
y
)
2
=
f
(
x
+
y
)
f
(
x
−
y
)
f(x)^2 -f(y)^2 =f(x+y)f(x-y)
f
(
x
)
2
−
f
(
y
)
2
=
f
(
x
+
y
)
f
(
x
−
y
)
for all
x
,
y
∈
R
.
x,y \in \mathbb{R}.
x
,
y
∈
R
.
Putnam
function
algebra
functional equation