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4
2017 Theme #4
2017 Theme #4
Source:
May 8, 2018
algebra
Problem Statement
Mary has a sequence
m
2
,
m
3
,
m
4
,
.
.
.
m_2,m_3,m_4,...
m
2
,
m
3
,
m
4
,
...
, such that for each
b
≥
2
b \ge 2
b
≥
2
,
m
b
m_b
m
b
is the least positive integer m for which none of the base-
b
b
b
logarithms
l
o
g
b
(
m
)
,
l
o
g
b
(
m
+
1
)
,
.
.
.
,
l
o
g
b
(
m
+
2017
)
log_b(m),log_b(m+1),...,log_b(m+2017)
l
o
g
b
(
m
)
,
l
o
g
b
(
m
+
1
)
,
...
,
l
o
g
b
(
m
+
2017
)
are integers. Find the largest number in her sequence.
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