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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 ...
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.
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]
A unitary perfect number is an integer which is the sum of its positive proper unitary divisors, not including the number itself. (A divisor d of a number n is a unitary divisor if d and n/d share no common factors). The number 6 is the only number that is both a perfect number and a unitary perfect number.
In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k , a number n is called k -perfect (or k -fold perfect) if the sum of all positive divisors of n (the divisor function , σ ( n )) is equal to kn ; a number is thus perfect if and ...
This is an accepted version of this page This is the latest accepted revision, reviewed on 20 January 2025. Practice and study of secure communication techniques "Secret code" redirects here. For the Aya Kamiki album, see Secret Code. "Cryptology" redirects here. For the David S. Ware album, see Cryptology (album). This article needs additional citations for verification. Please help improve ...
"For fundamental contributions to the theory and practice of cryptography and for educational leadership in cryptography." Andrew Odlyzko: 2012 "For pioneering contributions to cryptography and for service to the IACR." Manuel Blum: 2012 "For pioneering modern cryptography and for sustained contributions to cryptographic education." Eli Biham: 2012
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]