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Saudi Arabia Pre-TST + Training Tests
2011 Saudi Arabia Pre-TST
4.2
sum a_k (k!)^{2010}= (2011 !)^{2010}
sum a_k (k!)^{2010}= (2011 !)^{2010}
Source: 2011 Saudi Arabia Pre-TST February 4.2
January 1, 2022
number theory
factorial
Problem Statement
Find positive integers
a
1
<
a
2
<
.
.
.
<
a
2010
a_1 < a_2<... <a_{2010}
a
1
<
a
2
<
...
<
a
2010
such that
a
1
(
1
!
)
2010
+
a
2
(
2
!
)
2010
+
.
.
.
+
a
2010
(
2010
!
)
2010
=
(
2011
!
)
2010
.
a_1(1!)^{2010} + a_2(2!)^{2010} + ... + a_{2010}(2010!)^{2010} = (2011 !)^{2010}.
a
1
(
1
!
)
2010
+
a
2
(
2
!
)
2010
+
...
+
a
2010
(
2010
!
)
2010
=
(
2011
!
)
2010
.
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