What does automorphic number mean?
Definitions for automorphic number
au·to·mor·phic num·ber
This dictionary definitions page includes all the possible meanings, example usage and translations of the word automorphic number.
Wiktionary
automorphic numbernoun
A number whose decimal representation of its square ends in itself.
Wikipedia
Automorphic number
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose square "ends" in the same digits as the number itself.
Wikidata
Automorphic number
In mathematics an automorphic number is a number whose square "ends" in the same digits as number itself. For example, 5² = 25,6² = 36, 76² = 5776, and 890625² = 793212890625, so 5, 6, 76 and 890625 are all automorphic numbers. The sequence of automorphic numbers begins 1, 5, 6, 25, 76, 376, 625, 9376, .... Given a k-digit automorphic number, an automorphic number with at most 2k-digits can be found by from the formula: For k greater than 1, there are at most two automorphic numbers with k digits, one ending in 5 and one ending in 6. One of them has the form: and the other has the form: The sum of the two numbers is 10k + 1. The smaller of these two numbers may be less than 10k-1; for example with k = 4 the two numbers are 9376 and 625. In this case there is only one k digit automorphic number; the smaller number could only form a k digit automorphic number if a leading 0 were added to its digits. The following digit sequence can be used to find the two k-digit automorphic numbers, where . One automorphic number is found by taking the last k digits of this sequence; the second is found by subtracting the first number from .
Numerology
Chaldean Numerology
The numerical value of automorphic number in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of automorphic number in Pythagorean Numerology is: 5
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"automorphic number." Definitions.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.definitions.net/definition/automorphic+number>.
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