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1985 IMO Longlists
58
Prove that there exist infinitely many pairs (k,N)
Prove that there exist infinitely many pairs (k,N)
Source:
September 13, 2010
number theory unsolved
number theory
Problem Statement
Prove that there are infinitely many pairs
(
k
,
N
)
(k,N)
(
k
,
N
)
of positive integers such that
1
+
2
+
⋯
+
k
=
(
k
+
1
)
+
(
k
+
2
)
+
⋯
+
N
.
1 + 2 + \cdots + k = (k + 1) + (k + 2)+\cdots + N.
1
+
2
+
⋯
+
k
=
(
k
+
1
)
+
(
k
+
2
)
+
⋯
+
N
.
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