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A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

Let r and s be positive integers which are relatively prime and let a and b be any two integers. Then there is an integer N such that N=a (mod r) (1) and N=b (mod s). (2) ...

If a polynomial P(x) has a root x=a, i.e., if P(a)=0, then x-a is a factor of P(x).

A factor is a portion of a quantity, usually an integer or polynomial that, when multiplied by other factors, gives the entire quantity. The determination of factors is ...

In general, a remainder is a quantity "left over" after performing a particular algorithm. The term is most commonly used to refer to the number left over when two integers ...

If a polynomial P(x) is divided by (x-r), then the remainder is a constant given by P(r).

Given a Taylor series f(x)=f(x_0)+(x-x_0)f^'(x_0)+((x-x_0)^2)/(2!)f^('')(x_0)+... +((x-x_0)^n)/(n!)f^((n))(x_0)+R_n, (1) the error R_n after n terms is given by ...

If 1<=b<a and (a,b)=1 (i.e., a and b are relatively prime), then a^n-b^n has at least one primitive prime factor with the following two possible exceptions: 1. 2^6-1^6. 2. ...

Bézout's theorem for curves states that, in general, two algebraic curves of degrees m and n intersect in m·n points and cannot meet in more than m·n points unless they have ...

A proper factor of a positive integer n is a factor of n other than 1 or n (Derbyshire 2004, p. 32). For example, 2 and 3 are positive proper factors of 6, but 1 and 6 are ...