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Which of the following bases has the most automorphic numbers for the first 100 positive integers?

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An automorphic number is a number whose square ends in the same digits as the number itself. For example, the number 25 is an automorphic number (in base 10) because its square, 625, ends with the original number.

For the first 100 positive integers, five numbers are automorphic numbers for base 10 (1, 5, 6, 25, and 76), while only one number is automorphic for base 2 (1).

Which of the following bases has the most automorphic numbers for the first 100 positive integers?

a) 15
b) 6
c) 12
d) 7
e) 10

posted Apr 22 by anonymous

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