source : stackoverflow.com

## division – How to find the value of integer k efficiently for which q divides b ^ k finitely?

First of all, k will never equal zero unless q=1. k will never equal one unless q=b.

Next, if you can factorize q and b, then you can reason about them.

If there are any prime factors of b that are not factors of q at all, then k does not exist. Otherwise, k has to be large enough so that every factor of b^k is represented in q.

Here’s some pseudo-code:

if (q==1) return 0;

if (q==b) return 1;

// qfactors and bfactors are arrays, one element per factor

let qfactors = prime_factorization(q);

let bfactors = prime_factorization(b);

let kmin=0;

foreach (f in bfactors.unique) {

let bcount = bfactors.count(f);

let qcount = qfactors.count(f);

if (qcount==0 || qcount < bcount) return -1; // k does not exist

kmin_f = ceiling(bcount/qcount);

if (kmin_f > kmin) let kmin = kmin_f;

}

return kmin;

If k is an integer and (0.0025)( 0.025)( 0.00025)… – Magoosh GMAT – Written this way, we can see that in order for the product to be an integer, k must be equal to at least the positive of the power to which 10 is raised (-12). If k is less than 12, then the product will not be an integer.Integers are like whole numbers, but they also include negative numbers but still no fractions allowed! And when you only want positive integers, say "positive integers". It is not only accurate, it makes you sound intelligent. Like this (note: zero isn't positive or negative)Algebraic structure → Group theoryGroup theory. v. t. e. An integer (from the Latin integer meaning "whole") is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Whole Numbers and Integers – Assuming Variables is an important skill that is needed not only for Algebra but for solving any Quant question. Learn how to efficiently assume variables to get to the answer quickly and with high accuracy. Mar 13.The smallest integer #k# could be is #44# so that #756k# is a multiple of #1584#. As #756k# is a multiple of #1584#, it must have at least – two additional #2s# and one additional #11#.(Decimal to hex) Write a program that prompts the user to enter an integer between. 0 and 15 and displays its corresponding hex number. System.out.println(decimal + " is an invalid input")

Integer – Wikipedia – Re: k is an integer [#permalink] 27 Nov 2017, 11:47. 1. Expert Reply. We get: Quantity A: k (which is some number that's LESS THAN -2) Quantity B: -2. Answer: B. RELATED VIDEOS.55 60 25 30 35 40 Degrees (F) Which statement is the most appropriate comparison of the centers?dividing this by n-1 gives n+1-3/n-1. from there, we find all integers where 3/n-1 is an integer, thus we get n=-2, 0, 2, and 4.