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2021 Iran MO (2nd Round)
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2021 Iran MO (2nd Round)
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(1)
Fantastic numbers
Source: 2021 Iran second round mathematical Olympiad P2
5/15/2021
Call a positive integer
n
n
n
"Fantastic" if none of its digits are zero and it is possible to remove one of its digits and reach to an integer which is a divisor of
n
n
n
. ( for example , 25 is fantastic , as if we remove digit 2 , resulting number would be 5 which is divisor of 25 ) Prove that the number of Fantastic numbers is finite.
number theory
Digits