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3
2024 Team Problem 3
2024 Team Problem 3
Source:
April 23, 2024
team
Problem Statement
Define a function
f
:
N
→
N
f: \mathbb{N} \rightarrow \mathbb{N}
f
:
N
→
N
to be
f
(
x
)
=
(
x
+
1
)
!
−
x
!
f(x)=(x+1)!-x!
f
(
x
)
=
(
x
+
1
)!
−
x
!
. Find the number of positive integers
x
<
49
x<49
x
<
49
such that
f
(
x
)
f(x)
f
(
x
)
divides
f
(
49
)
f(49)
f
(
49
)
.Proposed by David Tang
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