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  2. List of Mersenne primes and perfect numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_Mersenne_primes...

    So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 1 + 2 + 3 = 6. [2] [4] Euclid proved c. 300 BCE that every prime expressed as M p = 2 p − 1 has a corresponding perfect number M p × (M p +1)/2 = 2 p − 1 × (2 p − 1). For example, the Mersenne prime 2 2 − 1 = 3 leads to the corresponding perfect number 2 2 ...

  3. Perfect number - Wikipedia

    en.wikipedia.org/wiki/Perfect_number

    In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.

  4. List of number theory topics - Wikipedia

    en.wikipedia.org/wiki/List_of_number_theory_topics

    Abundant number; Almost perfect number; Amicable number; Betrothed numbers; Deficient number; Quasiperfect number; Perfect number; Sociable number; Collatz conjecture; Digit sum dynamics Additive persistence; Digital root; Digit product dynamics Multiplicative digital root; Multiplicative persistence; Lychrel number; Perfect digital invariant ...

  5. Bibliography of cryptography - Wikipedia

    en.wikipedia.org/wiki/Bibliography_of_cryptography

    Covers more modern material and is aimed at undergraduates covering topics such as number theory and group theory not generally covered in cryptography books. Stinson, Douglas (2005). Cryptography: Theory and Practice ISBN 1-58488-508-4. Covers topics in a textbook style but with more mathematical detail than is usual. Young, Adam L. and Moti ...

  6. Computational hardness assumption - Wikipedia

    en.wikipedia.org/wiki/Computational_hardness...

    Computational hardness assumptions are of particular importance in cryptography. A major goal in cryptography is to create cryptographic primitives with provable security. In some cases, cryptographic protocols are found to have information theoretic security; the one-time pad is a common example. However, information theoretic security cannot ...

  7. Johannes Buchmann - Wikipedia

    en.wikipedia.org/wiki/Johannes_Buchmann

    In 1988, he proposed with Hugh C. Williams a cryptographic system based on the discrete logarithmic problem in the ideal class group of imaginary-square number fields (which, according to Carl Friedrich Gauss, is related to the theory of binary-square forms), which triggered further developments in cryptography with number fields. [5]

  8. Carl Pomerance - Wikipedia

    en.wikipedia.org/wiki/Carl_Pomerance

    Carl Bernard Pomerance (born 1944 in Joplin, Missouri) is an American number theorist.He attended college at Brown University and later received his Ph.D. from Harvard University in 1972 with a dissertation proving that any odd perfect number has at least seven distinct prime factors. [1]

  9. Joseph H. Silverman - Wikipedia

    en.wikipedia.org/wiki/Joseph_H._Silverman

    Silverman has published more than 100 research articles, written or coauthored six books, and edited three conference proceedings; his work has been cited more than 5000 times, by over 2000 distinct authors. [4] He has served on the editorial boards of Algebra and Number Theory and New York Journal of Mathematics. [5] [6]