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Algebraic number theory is the branch of number theory that deals with algebraic numbers. Historically, algebraic number theory developed as a set of tools for solving ...

Two complex numbers x=a+ib and y=c+id are multiplied as follows: xy = (a+ib)(c+id) (1) = ac+ibc+iad-bd (2) = (ac-bd)+i(ad+bc). (3) In component form, ...

Find a square number x^2 such that, when a given integer h is added or subtracted, new square numbers are obtained so that x^2+h=a^2 (1) and x^2-h=b^2. (2) This problem was ...

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."

A number n for which the product of divisors is equal to n^2. The first few are 1, 6, 8, 10, 14, 15, 21, 22, ... (OEIS A007422).

One of Cantor's ordinal numbers omega, omega+1, omega+2, ..., omega+omega, omega+omega+1, ... which is "larger" than any whole number.

There are two definitions of the Carmichael function. One is the reduced totient function (also called the least universal exponent function), defined as the smallest integer ...

The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.

If n>19, there exists a Poulet number between n and n^2. The theorem was proved in 1965.

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...