Number theory
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Number theory
Number theory is an important branch of mathematics.
It is interesting not only for the applications in cryptography, coding theory, etc, but also for the number of
open problems it contains.
German mathematician Carl Friedrich Gauss (1777–1855) said,
"Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
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Examples of open problems
Goldbach's conjecture. "Every even natural number greater than 2 is the sum of two prime numbers."
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 first few perfect numbers are 6, 28, 496 and 8128.
It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist.
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