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2013 BMT Spring
13
2013 BMT Individual 13
2013 BMT Individual 13
Source:
January 18, 2022
algebra
Problem Statement
Let
f
(
n
)
f(n)
f
(
n
)
be a function from integers to integers. Suppose
f
(
11
)
=
1
f(11) = 1
f
(
11
)
=
1
, and
f
(
a
)
f
(
b
)
=
f
(
a
+
b
)
+
f
(
a
ā
b
)
f(a)f(b) = f(a +b) + f(a - b)
f
(
a
)
f
(
b
)
=
f
(
a
+
b
)
+
f
(
a
ā
b
)
, for all integers
a
,
b
a, b
a
,
b
. Find
f
(
2013
)
f(2013)
f
(
2013
)
.
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