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  • A '''prime number''' (or simply '''prime''') is a [[positive integer]] <math>p>1</math> whose ...osite number|composite]] because it is its only factor among the [[natural number|natural numbers]].
    7 KB (1,080 words) - 18:00, 21 February 2025
  • ...one of the ten [[digit]]s is the last to appear in the units position of a number in the Fibonacci sequence?<br><br><math> \mathrm{(A) \ 0 } \qquad \mathrm{( ...th. An offspring rabbit takes one month to grow up. Find a formula for the number of rabbits (including offspring) in the <math>n</math>th month.
    7 KB (1,111 words) - 13:57, 24 June 2024
  • '''Lucas' Theorem''' states that for any [[prime]] <math>p</math> and any [[positive [[Category:Number theory]]
    1 KB (251 words) - 14:13, 11 August 2020
  • ...}</math> is the [[Fibonacci sequence]] and <math>\{ L_k \}</math> is the [[Lucas sequence]]. <math>\blacksquare</math> [[Category:Olympiad Number Theory Problems]]
    3 KB (448 words) - 20:41, 23 April 2008
  • ...perator to an eigenvector causes the eigenvector to dilate. The associated number <math>\lambda</math> is called the [[eigenvalue]]. For example, let <math>F_n</math> be the <math>n</math>th [[Fibonacci number]] defined by <math>F_1 = F_2 = 1</math>, and
    19 KB (3,412 words) - 13:57, 21 September 2022
  • A Mersenne [[Prime number|prime]] is a prime that is in the form of <math>2^n-1</math>, where <math>n ...ain factor: There is an integer bit value set to that, so that the largest number with a certain amount of bits is a form of <math>2^n-1</math>.
    2 KB (318 words) - 09:29, 26 February 2020
  • A number which when divided by <math>10</math> leaves a remainder of <math>9</math>, ...<math>1</math> through <math>10</math> is <math>2520</math>, therefore the number we want to find is <math>2520-1=\boxed{\textbf{(D)}\ 2519}</math>
    932 bytes (136 words) - 16:27, 19 September 2022
  • Alternate Case <math>4:</math> Use complementary counting. Total number of ways to choose 3 people from 8 which is <math>\dbinom{8}{3}</math>. Sub- ...ing people are separated by sitting people. We just need to determine the number of combinations of pairs and singles and the problem becomes very similar t
    11 KB (1,724 words) - 14:29, 13 October 2024
  • ...od 2 in problem 77, we see that each that the base 2 representation of the number reveals to us how many times we end up applying the ...m of <math>O_{2008}=2^7\cdot O_{0}=2^7=128</math>. So we need to count the number of integers between <math>\{0,2009\}</math> which
    2 KB (234 words) - 14:09, 1 August 2021
  • ...x=8.</math> Thus, there is only <math>\boxed{\textbf{(B) }1}</math> cuddly number, which is <math>89.</math> ...get that there is only <math>\boxed{\textbf{(B) }1}</math> 2-digit cuddly number, and it is <math>89</math>. Yay!!!
    2 KB (306 words) - 02:35, 8 September 2024
  • The six-digit number <math>\underline{2}\,\underline{0}\,\underline{2}\,\underline{1}\,\underlin Any number ending in <math>5</math> is divisible by <math>5</math>. So we can eliminat
    3 KB (491 words) - 20:13, 12 July 2023
  • The number of scalene triangles having all sides of integral lengths, and perimeter le ~Lucas
    690 bytes (93 words) - 16:29, 19 September 2022
  • Compute the number of ways to arrange <math>2</math> distinguishable apples and <math>5</math> ...<math>1,2,3,4,5,6,7,8,9,10</math>, respectively. Find the probability that Lucas would not sit next to Michael595 AND Michael595 chose an even seat.
    13 KB (2,097 words) - 16:38, 29 April 2021
  • ...+ F_{2i - 2} + 1}{5} = \frac {L_{2i - 1} + 1}{5},</cmath> where L is Lucas number, so sequence of Lucas numbers modulo <math>5</math> is periodic, the period is <math>4,</math> an
    15 KB (2,351 words) - 07:28, 20 April 2023