| 11. | The fundamental theorem of arithmetic says that every positive integer has a single unique prime factorization.
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| 12. | The integer factorization problem is the computational problem of determining the prime factorization of a given integer.
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| 13. | The number of factors of " b n " is given using its prime factorization.
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| 14. | As noted prime factorization are also inefficient; many modern cryptography systems even rely on that inefficiency.
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| 15. | This contradiction shows that " s " does not actually have two different prime factorizations.
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| 16. | This characterization makes it possible to determine whether a number is practical by examining its prime factorization.
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| 17. | A "'septimal comma "'is a small seven in its prime factorization.
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| 18. | The asymptotically best efficiency is obtained by computing " n " ! from its prime factorization.
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| 19. | In order to find the greatest common divisor, the Euclidean algorithm or prime factorization may be used.
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| 20. | The prime factorization of twenty is 2 2 ?5, so it is not a perfect power.
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