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  • ..., the principle may be referred to as the '''Dirichlet box principle'''. A common phrasing of the principle uses balls and boxes and is that if <math>n</math ...at two numbers will share the same <math>b</math> value. These numbers are multiples—if we define the two numbers <math>2^ib</math> and <math>2^jb</math> wher
    11 KB (1,980 words) - 21:39, 19 February 2025
  • ...ath>7</math> are the only primes that form an [[Arithmetic sequence]] with common difference 2. ...th>11</math> are the only primes that form an [[Arithmetic sequence]] with common difference 4.
    7 KB (1,080 words) - 18:00, 21 February 2025
  • * [[base numbers/Common bases | Common bases]] ...and 60 seconds in a minute (they might have used it because it has so many multiples, 12 in fact, we wouldn't want any fractions). The [[Roman system]], which
    4 KB (547 words) - 16:23, 30 December 2020
  • What are multiples and diVisors: https://youtu.be/ij5_vWBxZoU ...nteger has an [[infinite]] number of multiples. As an example, some of the multiples of 15 are 15, 30, 45, 60, and 75.
    860 bytes (142 words) - 21:51, 26 January 2021
  • ...them. Any [[finite]] [[set]] of integers has an [[infinite]] number of [[common multiple]]s, but only one LCM. The LCM of a set of numbers <math>\{a_1,a_2, == Video on Least Common Multiple ==
    2 KB (383 words) - 09:49, 4 September 2022
  • A common [[Brute forcing|bruteforce]] technique with inequalities is to clear denomi ...lting matrices, eventually all entries of <math>D</math> are canceled. The multiples of the permutation matrices subtracted give the representation <math>D=\sum
    11 KB (1,786 words) - 08:03, 22 February 2025
  • ...</math> is [[geometric sequence|geometric]] with <math> a_1=a </math> and common [[ratio]] <math> r, </math> where <math> a </math> and <math> r </math> are ...<math>11</math> from <math>11</math> to <math>1001</math>. Since the odd multiples are separated by a distance of <math>22</math>, the number of ordered pairs
    4 KB (651 words) - 17:27, 22 May 2021
  • How many positive integers not exceeding <math>2001</math> are multiples of <math>3</math> or <math>4</math> but not <math>5</math>? ...such trip? (Note: Two edges of a tetrahedron are opposite if they have no common endpoint.)
    13 KB (1,957 words) - 11:53, 24 January 2024
  • ...egers]] and an introductory study of number theory involves exploring many common relationships between integers. *** [[Common divisor]]s
    2 KB (195 words) - 15:20, 2 March 2008
  • ...h>. Thus the number of potential values of <math>n</math> is the number of multiples of <math>9</math> from <math>0</math> to <math>1000</math>, or <math>112</m ...o find distinct <math>n</math>'s so let's subtract the cases where we find common values , from the total number of values.
    11 KB (1,857 words) - 11:57, 18 July 2024
  • The [[least common multiple]] of <math>18</math> and <math>48</math> is <math>144</math>, so d ...math>a,b</math>, the largest number that cannot be expressed as the sum of multiples of <math>a,b</math> is <math>a \cdot b - a - b</math>. For <math>3,8</math>
    3 KB (564 words) - 03:47, 4 August 2023
  • Thus, for a given value of <math>y</math>, we need the number of multiples of <math>y(y+1)</math> from <math>0</math> to <math>100-y</math> (as <math> ...> must be integers. Since <math>y</math> and <math>y+1</math> cannot share common prime factors, it follows that <math>\frac{x-y}{y(y+1)}</math> must also be
    4 KB (646 words) - 11:20, 28 December 2024
  • Denoting the greatest common divisor of <math>a, b </math> as <math>(a,b) </math>, we use the [[Euclidea Their greatest common divisor is 1, so <math>\frac{21n+4}{14n+3}</math> is irreducible. Q.E.D.
    5 KB (767 words) - 09:59, 23 July 2023
  • As in the previous solution, none of the six consecutive numbers can be multiples of <math>7</math>. This means that together, they take on the values <math and <math>p^2 + 3</math> have no common factors (since they differ
    10 KB (1,617 words) - 19:44, 2 December 2024
  • ...math> smallest positive multiples of <math>6</math>. How many elements are common to <math>S</math> and <math>T</math>? ...on multiple]] <math>\mathrm{lcm}(4,6)=12</math>, the [[element]]s that are common to <math>S</math> and <math>T</math> must be [[multiple]]s of <math>12</mat
    1 KB (220 words) - 11:55, 14 December 2021
  • ...inite]] [[set]] of positive integers have an [[infinite]] number of common multiples. Every common multiple of a set of integers is a multiple of the [[least common multiple]] of those integers.
    692 bytes (106 words) - 10:15, 19 April 2008
  • ...math> smallest positive multiples of <math>6</math>. How many elements are common to <math>S</math> and <math>T</math>?
    14 KB (2,026 words) - 10:45, 12 July 2021
  • == Common Pythagorean Triples == These are some common Pythagorean triples:
    4 KB (684 words) - 15:45, 1 August 2020
  • The second definition of the Carmichael function is the least common multiples of all the factors of <math>\phi(n)</math>. It is written as <math>\lambda'
    2 KB (258 words) - 10:56, 1 August 2022
  • How many positive perfect squares less than <math>10^6</math> are multiples of 24? ...>C</math> lies on the positive <math>y</math>-axis, the area of the region common to the original and the rotated triangle is in the form <math>p\sqrt{2} + q
    7 KB (1,218 words) - 14:28, 11 July 2022

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