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2024 CMIMC
2024 CMIMC Algebra and Number Theory
1
1
Part of
2024 CMIMC Algebra and Number Theory
Problems
(1)
2024 Alg/NT Problem 1
Source:
4/14/2024
Connor is thinking of a two-digit number
n
n
n
, which satisfies the following properties:[*] If
n
>
70
n>70
n
>
70
, then
n
n
n
is a perfect square. [*] If
n
>
40
n>40
n
>
40
, then
n
n
n
is prime. [*] If
n
<
80
n<80
n
<
80
, then the sum of the digits of
n
n
n
is
14
14
14
.What is Connor's number?Proposed by Connor Gordon
number theory