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ISI B.Math Entrance Exam
2008 ISI B.Math Entrance Exam
4
B.Math 2008-Pigeonhole
B.Math 2008-Pigeonhole
Source:
April 16, 2012
pigeonhole principle
Problem Statement
Let
a
1
,
a
2
,
.
.
.
,
a
n
a_1,a_2,...,a_n
a
1
,
a
2
,
...
,
a
n
be integers . Show that there exists integers
k
k
k
and
r
r
r
such that the sum
a
k
+
a
k
+
1
+
.
.
.
+
a
k
+
r
a_k+a_{k+1}+...+a_{k+r}
a
k
+
a
k
+
1
+
...
+
a
k
+
r
is divisible by
n
n
n
.
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