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Putnam
1977 Putnam
A3
A3
Part of
1977 Putnam
Problems
(1)
Putnam 1977 A3
Source:
4/7/2022
Let
u
,
f
u,f
u
,
f
and
g
g
g
be functions, defined for all real numbers
x
x
x
, such that
u
(
x
+
1
)
+
u
(
x
−
1
)
2
=
f
(
x
)
and
u
(
x
+
4
)
+
u
(
x
−
4
)
2
=
g
(
x
)
.
\frac{u(x+1)+u(x-1)}{2}=f(x) \text{ and } \frac{u(x+4)+u(x-4)}{2}=g(x).
2
u
(
x
+
1
)
+
u
(
x
−
1
)
=
f
(
x
)
and
2
u
(
x
+
4
)
+
u
(
x
−
4
)
=
g
(
x
)
.
Determine
u
(
x
)
u(x)
u
(
x
)
in terms of
f
f
f
and
g
g
g
.
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