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5 Analytic number theory: additive problems. ... This is a list of topics in number theory. See also: ... Almost perfect number;
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.
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 ...
However, in cryptography, code has a more specific meaning: the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a code word (for example, "wallaby" replaces "attack at dawn"). A cypher, in contrast, is a scheme for changing or substituting an element below such a level (a letter, a syllable, or a pair of letters, etc ...
Notably, absent consensus, please do not add articles about individual perfect numbers themselves (such as 6). Pages in category "Perfect numbers" The following 11 pages are in this category, out of 11 total.
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 ...
For example, in the Diffie–Hellman key exchange, an eavesdropper observes and exchanged as part of the protocol, and the two parties both compute the shared key . A fast means of solving the DHP would allow an eavesdropper to violate the privacy of the Diffie–Hellman key exchange and many of its variants, including ElGamal encryption .