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2006 Singapore MO Open
5
Divides
Divides
Source: Singapore Mathematical Olympiad 2006 Problem 5
July 7, 2006
number theory proposed
number theory
Problem Statement
Let
a
,
b
,
n
a,b,n
a
,
b
,
n
be positive integers. Prove that
n
!
n!
n
!
divides
b
n
−
1
a
(
a
+
b
)
(
a
+
2
b
)
.
.
.
(
a
+
(
n
−
1
)
b
)
b^{n-1}a(a+b)(a+2b)...(a+(n-1)b)
b
n
−
1
a
(
a
+
b
)
(
a
+
2
b
)
...
(
a
+
(
n
−
1
)
b
)
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