| 11. | 25 is a centered octagonal number, a centered square number, and an automorphic number.
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| 12. | For example, = 3, so 9 is a square number.
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| 13. | Where \ Box is the set of square numbers.
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| 14. | The square of an integer may also be called a square number or a perfect square.
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| 15. | All centered square numbers and their divisors have a remainder of one when divided by four.
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| 16. | More precisely, because of the identity, the difference between the th and the th square number is.
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| 17. | It is a square number, being 76.
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| 18. | :This idea is originally due to Galileo ( who used square numbers instead of nonsquare semiprimes ).
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| 19. | Hence all centered square numbers and their divisors end with digits 1 or 5 in base 12.
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| 20. | Thirty has but one number for which it is the aliquot sum : the square number 841.
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