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Problems
Contests
National and Regional Contests
PEN Problems
PEN P Problems
38
38
Part of
PEN P Problems
Problems
(1)
P 38
Source:
5/25/2007
Find the smallest possible
n
n
n
for which there exist integers
x
1
x_{1}
x
1
,
x
2
x_{2}
x
2
,
⋯
\cdots
⋯
,
x
n
x_{n}
x
n
such that each integer between
1000
1000
1000
and
2000
2000
2000
(inclusive) can be written as the sum (without repetition), of one or more of the integers
x
1
x_{1}
x
1
,
x
2
x_{2}
x
2
,
⋯
\cdots
⋯
,
x
n
x_{n}
x
n
.
Additive Number Theory