Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
If , where for all and ,…
MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions
Problem
If
∑
k
=
1
n
f
(
a
+
k
)
=
16
(
2
n
−
1
)
\sum_{k=1}^n f(a+k)=16(2^n-1)
∑
k
=
1
n
f
(
a
+
k
)
=
16
(
2
n
−
1
)
, where
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
f(x+y)=f(x)f(y)
f
(
x
+
y
)
=
f
(
x
)
f
(
y
)
for all
x
,
y
∈
N
x,y\in\mathbb{N}
x
,
y
∈
N
and
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
, then
f
(
a
)
=
f(a)=
f
(
a
)
=
(a) 8 (b) 6 (c) 4 (d) 2
Related theory
Functions
Browse the problem library