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Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Ukraine National Mathematical Olympiad
2021 Ukraine National Mathematical Olympiad
10.5
10.5
Part of
2021 Ukraine National Mathematical Olympiad
Problems
(1)
all sets of n consecutive integers {a+1,a+2,...,a+n} in which one =sum of others
Source: 2021 Ukraine NMO 10.5
4/4/2021
Find all sets of
n
≥
2
n\ge 2
n
≥
2
consecutive integers
{
a
+
1
,
a
+
2
,
.
.
.
,
a
+
n
}
\{a+1,a+2,...,a+n\}
{
a
+
1
,
a
+
2
,
...
,
a
+
n
}
where
a
∈
Z
a\in Z
a
∈
Z
, in which one of the numbers is equal to the sum of all the others.(Bogdan Rublev)
number theory
Sum