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2021 CMIMC
8
2021 Team P8
2021 Team P8
Source:
March 2, 2021
algebra
number theory
Problem Statement
Determine the number of functions
f
f
f
from the integers to
{
1
,
2
,
⋯
,
15
}
\{1,2,\cdots,15\}
{
1
,
2
,
⋯
,
15
}
which satisfy
f
(
x
)
=
f
(
x
+
15
)
f(x)=f(x+15)
f
(
x
)
=
f
(
x
+
15
)
and
f
(
x
+
f
(
y
)
)
=
f
(
x
−
f
(
y
)
)
f(x+f(y))=f(x-f(y))
f
(
x
+
f
(
y
))
=
f
(
x
−
f
(
y
))
for all
x
,
y
x,y
x
,
y
.Proposed by Vijay Srinivasan
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