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Moldova Team Selection Test
1997 Moldova Team Selection Test
9
3 Nov FE problem
3 Nov FE problem
Source:
November 3, 2016
function
algebra
Problem Statement
Find all
t
∈
Z
t\in \mathbb Z
t
∈
Z
such that: exists a function
f
:
Z
+
→
Z
f:\mathbb Z^+\to \mathbb Z
f
:
Z
+
→
Z
such that:
f
(
1997
)
=
1998
f(1997)=1998
f
(
1997
)
=
1998
∀
x
,
y
∈
Z
+
,
gcd
(
x
,
y
)
=
d
:
f
(
x
y
)
=
f
(
x
)
+
f
(
y
)
+
t
f
(
d
)
:
P
(
x
,
y
)
\forall x,y\in \mathbb Z^+ , \text{gcd}(x,y)=d : f(xy)=f(x)+f(y)+tf(d):P(x,y)
∀
x
,
y
∈
Z
+
,
gcd
(
x
,
y
)
=
d
:
f
(
x
y
)
=
f
(
x
)
+
f
(
y
)
+
t
f
(
d
)
:
P
(
x
,
y
)
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