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The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; [2] [3] this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4. If any number ends in a two digit number that ...
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21). If m is a divisor of n, then so is −m. The tables below only ...
For example, assume that your random number source gives numbers from 0 to 99 (as was the case for Fisher and Yates' original tables), which is 100 values, and that you wish to obtain an unbiased random number from 0 to 15 (16 values). If you simply divide the numbers by 16 and take the remainder, you will find that the numbers 0–3 occur ...
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. [ 1 ] For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0 ...
For example, σ 0 (12) is the number of the divisors of 12: ... and a i is the maximum power of p i by which n is divisible, ... Refactorable number; Table of ...
If m is a power of 2, then a − 1 should be divisible by 4 but not divisible by 8, i.e. a ≡ 5 (mod 8). [ 1 ] : §3.2.1.3 Indeed, most multipliers produce a sequence which fails one test for non-randomness or another, and finding a multiplier which is satisfactory to all applicable criteria [ 1 ] : §3.3.3 is quite challenging. [ 8 ]
For example: If one were to attempt to square 738 and calculated 54,464, a quick sanity check could show that this result cannot be true. Consider that 700 < 738, yet 700 2 = 7 2 × 100 2 = 490,000 > 54,464. Since squaring positive integers preserves their inequality, the result cannot be true, and so the calculated result is incorrect.
The following is pseudocode which combines Atkin's algorithms 3.1, 3.2, and 3.3 [1] by using a combined set s of all the numbers modulo 60 excluding those which are multiples of the prime numbers 2, 3, and 5, as per the algorithms, for a straightforward version of the algorithm that supports optional bit-packing of the wheel; although not specifically mentioned in the referenced paper, this ...