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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2017 India PRMO
29
Number Theory
Number Theory
Source: PRMO 2017
September 16, 2017
number theory
Problem Statement
For each positive integer
n
n
n
, consider the highest common factor
h
n
h_n
h
n
ā
of the two numbers
n
!
+
1
n!+1
n
!
+
1
and
(
n
+
1
)
!
(n+1)!
(
n
+
1
)!
. For
n
<
100
n<100
n
<
100
, find the largest value of
h
n
h_n
h
n
ā
.
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