Search results
Results from the WOW.Com Content Network
Chinese remainder theorem. Sunzi's original formulation: x ≡ 2 (mod 3) ≡ 3 (mod 5) ≡ 2 (mod 7) with the solution x = 23 + 105k, with k an integer. In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the ...
A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.
(Figure 2) Illustration of numerical integration for the equation ′ =, = Blue is the Euler method; green, the midpoint method; red, the exact solution, =. The step size is =
Mathematics. Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [1]
Chinese remainder theorem: The Chinese remainder theorem, including simultaneous congruences in number theory, was first created in the 3rd century AD in the mathematical book Sunzi Suanjing posed the problem: "There is an unknown number of things, when divided by 3 it leaves 2, when divided by 5 it leaves 3, and when divided by 7 it leaves a ...
The rings for which such a theorem exists are called Euclidean domains, but in this generality, uniqueness of the quotient and remainder is not guaranteed. [8] Polynomial division leads to a result known as the polynomial remainder theorem: If a polynomial f(x) is divided by x − k, the remainder is the constant r = f(k). [9] [10]
Shimura's reciprocity law. Siegel–Weil formula. Siegel's theorem on integral points. Six exponentials theorem. Skolem–Mahler–Lech theorem. Sophie Germain's theorem. Størmer's theorem. Subspace theorem. Sum of two squares theorem.
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...