MathDB
Problems
Contests
Undergraduate contests
Miklós Schweitzer
2004 Miklós Schweitzer
4
4
Part of
2004 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 2004, Problem 4
Source: Miklós Schweitzer 2004
7/30/2016
Determine all totally multiplicative and non-negative functions
f
:
Z
→
Z
f\colon\mathbb{Z}\rightarrow \mathbb{Z}
f
:
Z
→
Z
with the property that if
a
,
b
∈
Z
a, b\in \mathbb{Z}
a
,
b
∈
Z
and
b
≠
0
b\neq 0
b
=
0
, then there exist integers
q
q
q
and
r
r
r
such that
a
−
q
b
+
r
a-qb+r
a
−
q
b
+
r
and
f
(
r
)
<
f
(
b
)
f(r)<f(b)
f
(
r
)
<
f
(
b
)
.
college contests
Miklos Schweitzer
function