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Putnam
2017 Putnam
B2
B2
Part of
2017 Putnam
Problems
(1)
Putnam 2017 B2
Source:
12/3/2017
Suppose that a positive integer
N
N
N
can be expressed as the sum of
k
k
k
consecutive positive integers
N
=
a
+
(
a
+
1
)
+
(
a
+
2
)
+
⋯
+
(
a
+
k
−
1
)
N=a+(a+1)+(a+2)+\cdots+(a+k-1)
N
=
a
+
(
a
+
1
)
+
(
a
+
2
)
+
⋯
+
(
a
+
k
−
1
)
for
k
=
2017
k=2017
k
=
2017
but for no other values of
k
>
1.
k>1.
k
>
1.
Considering all positive integers
N
N
N
with this property, what is the smallest positive integer
a
a
a
that occurs in any of these expressions?
Putnam
Putnam 2017