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National and Regional Contests
Turkey Contests
Turkey Team Selection Test
1990 Turkey Team Selection Test
5
m-b_m = 1990
m-b_m = 1990
Source: Turkey TST 1990 - P5
September 11, 2013
number theory proposed
number theory
Problem Statement
Let
b
m
b_m
b
m
be numbers of factors
2
2
2
of the number
m
!
m!
m
!
(that is,
2
b
m
∣
m
!
2^{b_m}|m!
2
b
m
∣
m
!
and
2
b
m
+
1
∤
m
!
2^{b_m+1}\nmid m!
2
b
m
+
1
∤
m
!
). Find the least
m
m
m
such that
m
−
b
m
=
1990
m-b_m = 1990
m
−
b
m
=
1990
.
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