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Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1993 Moldova Team Selection Test
9
9
Part of
1993 Moldova Team Selection Test
Problems
(1)
Determine the greatest integer $m$ for which $2102$ is $m$-additive
Source: Moldova TST 1993
8/8/2023
Positive integer
q
q{}
q
is
m
−
a
d
d
i
t
i
v
e
m-additive
m
−
a
dd
i
t
i
v
e
(
m
∈
N
,
m
≥
2
)
(m\in\mathbb{N}, m\geq2)
(
m
∈
N
,
m
≥
2
)
if there exist pairwise distinct positive integers
a
1
,
a
2
,
…
,
a
m
a_1,a_2,\ldots,a_m
a
1
,
a
2
,
…
,
a
m
such that
q
=
a
1
+
a
2
+
…
+
a
m
q=a_1+a_2+\ldots+a_m
q
=
a
1
+
a
2
+
…
+
a
m
and
a
i
∣
a
i
+
1
a_i | a_{i+1}
a
i
∣
a
i
+
1
for
i
=
1
,
2
,
…
,
m
−
1
i=1,2,\ldots,m-1
i
=
1
,
2
,
…
,
m
−
1
. a) Prove that
1993
1993
1993
is
8
8
8
-additive, but
9
9
9
-additive. b) Determine the greatest integer
m
m
m
for which
2102
2102
2102
is
m
m
m
-additive.
number theory