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IMO LongList 1985 BUL2 - Prove that the fraction is integer
IMO LongList 1985 BUL2 - Prove that the fraction is integer
Source:
September 10, 2010
floor function
number theory unsolved
number theory
Problem Statement
Let
a
a
a
and
b
b
b
be integers and
n
n
n
a positive integer. Prove that
b
n
−
1
a
(
a
+
b
)
(
a
+
2
b
)
⋯
(
a
+
(
n
−
1
)
b
)
n
!
\frac{b^{n-1}a(a + b)(a + 2b) \cdots (a + (n - 1)b)}{n!}
n
!
b
n
−
1
a
(
a
+
b
)
(
a
+
2
b
)
⋯
(
a
+
(
n
−
1
)
b
)
is an integer.
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