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Iran-Singapore-Taiwan Friendly Math Competition
2022 Iran-Taiwan Friendly Math Competition
6
6
Part of
2022 Iran-Taiwan Friendly Math Competition
Problems
(1)
Euclidian algorithm-ish function
Source: 2022 IRN TWN Friendly math competition P6
6/23/2022
Find all completely multipiclative functions
f
:
Z
→
Z
⩾
0
f:\mathbb{Z}\rightarrow \mathbb{Z}_{\geqslant 0}
f
:
Z
→
Z
⩾
0
such that for any
a
,
b
∈
Z
a,b\in \mathbb{Z}
a
,
b
∈
Z
and
b
≠
0
b\neq 0
b
=
0
, there exist integers
q
,
r
q,r
q
,
r
such that
a
=
b
q
+
r
a=bq+r
a
=
b
q
+
r
and
f
(
r
)
<
f
(
b
)
f(r)<f(b)
f
(
r
)
<
f
(
b
)
Proposed by Navid Safaei
function
number theory
algebra
Iran
Taiwan