- remainder theorem
- noun Date: 1886 a theorem in algebra: if f(x) is a polynomial in x then the remainder on dividing f(x) by x - a is f(a)
New Collegiate Dictionary. 2001.
remainder theorem
Look at other dictionaries:
remainder theorem — noun : a theorem in algebra: if f(x) is a polynomial in x then the remainder on dividing f(x) by x a is f(a) … Useful english dictionary
Chinese remainder theorem — The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. In its most basic form it concerned with determining n, given the remainders generated by division of n by several numbers.… … Wikipedia
Polynomial remainder theorem — The polynomial remainder theorem in algebra is an application of polynomial long division. It states that the remainder, r,, of a polynomial, f(x),, divided by a linear divisor, x a,, is equal to f(a) ,.This follows from the definition of… … Wikipedia
Chinese remainder theorem — ▪ mathematics ancient theorem that gives the conditions necessary for multiple equations to have a simultaneous integer solution. The theorem has its origin in the work of the 3rd century AD Chinese mathematician Sun Zi, although the… … Universalium
Remainder — In arithmetic, when the result of the division of two integers cannot be expressed with an integer quotient, the remainder is the amount left over. The remainder for natural numbers If a and d are natural numbers, with d non zero, it can be… … Wikipedia
Malgrange preparation theorem — In mathematics, the Malgrange preparation theorem is an analogue of the Weierstrass preparation theorem for smooth functions. It was conjectured by René Thom and proved by B. Malgrange (1962–1963, 1964, 1967). Contents 1 Statement of… … Wikipedia
Weierstrass preparation theorem — In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at P, a polynomial… … Wikipedia
Structure theorem for finitely generated modules over a principal ideal domain — In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that… … Wikipedia
Factor theorem — In algebra, the factor theorem is a theorem for finding out the factors of a polynomial (an expression in which the terms are only added, subtracted or multiplied, e.g. x^2 + 6x + 6). It is a special case of the polynomial remainder theorem. The… … Wikipedia
Linear congruence theorem — In modular arithmetic, the question of when a linear congruence can be solved is answered by the linear congruence theorem. If a and b are any integers and n is a positive integer, then the congruence: ax equiv; b (mod n ) (1)has a solution for x … Wikipedia
