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EGMO TST - Moldova
2018 Moldova EGMO TST
4
Number Theory problem
Number Theory problem
Source: EGMO 2018 Moldova TST
February 11, 2018
number theory
Problem Statement
Find all sets of positive integers
A
=
{
a
1
,
a
2
,
.
.
.
a
19
}
A=\big\{ a_1,a_2,...a_{19}\big\}
A
=
{
a
1
,
a
2
,
...
a
19
}
which satisfy the following:
1
)
a
1
+
a
2
+
.
.
.
+
a
19
=
2017
;
1\big) a_1+a_2+...+a_{19}=2017;
1
)
a
1
+
a
2
+
...
+
a
19
=
2017
;
2
)
S
(
a
1
)
=
S
(
a
2
)
=
.
.
.
=
S
(
a
19
)
2\big) S(a_1)=S(a_2)=...=S(a_{19})
2
)
S
(
a
1
)
=
S
(
a
2
)
=
...
=
S
(
a
19
)
where
S
(
n
)
S\big(n\big)
S
(
n
)
denotes digit sum of number
n
n
n
.
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