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Danube Competition in Mathematics
2015 Danube Mathematical Competition
4
Nice problem
Nice problem
Source:
September 5, 2017
number theory
Problem Statement
Given an integer
n
≥
2
n \ge 2
n
≥
2
,determine the numbers that written in the form
a
1
a_1
a
1
a
2
a_2
a
2
+
+
+
a
2
a_2
a
2
a
3
a_3
a
3
+
+
+
.
.
.
...
...
a
k
−
1
a_{k-1}
a
k
−
1
a
k
a_k
a
k
, where
k
k
k
is an integer greater than or equal to 2, and
a
1
a_1
a
1
,...
a
k
a_k
a
k
are positive integers with sum
n
n
n
.
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