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In this case, s is called the least absolute remainder. [3] As with the quotient and remainder, k and s are uniquely determined, except in the case where d = 2n and s = ± n. For this exception, we have: a = k⋅d + n = (k + 1)d − n. A unique remainder can be obtained in this case by some convention—such as always taking the positive value ...
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
The pseudo-remainder of the pseudo-division of two polynomials in Z[X] belongs always to Z[X]. A pseudo-remainder sequence is the sequence of the (pseudo) remainders r i obtained by replacing the instruction +:= (,) of Euclid's algorithm by +:= (,), where α is an element of Z that divides exactly every coefficient of the numerator.
Polynomial long division can be used to find the equation of the line that is tangent to the graph of the function defined by the polynomial P(x) at a particular point x = r. [3] If R(x) is the remainder of the division of P(x) by (x – r) 2, then the equation of the tangent line at x = r to the graph of the function y = P(x) is y = R(x ...
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
The stack levels are named X (the bottom), Y, Z, and T (the top); they have no connection with the variables of the same names. Level X appears on the lower line of the display and level Y on the upper line. Each stack level can contain any of the data types supported by the machine: real number, complex number, or vector.
Another method is multiplication by 3. A number of the form 10x + y has the same remainder when divided by 7 as 3x + y. One must multiply the leftmost digit of the original number by 3, add the next digit, take the remainder when divided by 7, and continue from the beginning: multiply by 3, add the next digit, etc.
The HP Voyager series calculator are keystroke programmable, meaning that it can remember and later execute sequences of keystrokes to solve particular problems of interest to the user. These keystroke programs, in addition to performing any operation normally available on the keyboard, can also make use of conditional and unconditional ...