Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
For
k
∈
{
0
,
1
,
2
,
3
}
k\in\{0,1,2,3\}
k
∈
{
0
,
1
,
2
,
3
}
, define the function
f
k
:
{
1
,
2
,
3
,
4
}
→
{
1
,
2
,
3
,
4
}
f_k:\{1,2,3,4\}\to\{1,2,3,4\}
f
k
:
{
1
,
2
,
3
,
4
}
→
{
1
,
2
,
3
,
4
}
by
f
k
(
i
)
=
(
(
i
+
k
)
m
o
d
4
)
+
1.
f_k(i)=\bigl((i+k)\bmod 4\bigr)+1.
f
k
(
i
)
=
(
(
i
+
k
)
mod
4
)
+
1.
Identify all values of
k
k
k
for which
f
k
f_k
f
k
is bijective.
Browse the problem library