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2023 LMT Fall
16
16
Part of
2023 LMT Fall
Problems
(1)
2023 Fall LMT Speed p16 , number in base 10,11,12
Source:
3/2/2024
Jeff writes down the two-digit base-
10
10
10
prime
a
b
10
‾
\overline{ab_{10}}
a
b
10
. He realizes that if he misinterprets the number as the base
11
11
11
number
a
b
11
‾
\overline{ab_{11}}
a
b
11
or the base
12
12
12
number
a
b
12
‾
\overline{ab_{12}}
a
b
12
, it is still a prime. What is the least possible value of Jeff’s number (in base
10
10
10
)?Proposed byMuztaba Syed
number theory