Create the page "N^4 4" on this wiki! See also the search results found.

• Euler's Totient Theorem
  ...range <math>\{1,2,3\cdots{,n}\}</math> which are relatively prime to <math>n</math>. If <math>{a}</math> is an integer and <math>m</math> is a positive ...{k}\equiv 1\pmod{n}</math>, and by [[Lagrange's Theorem]] <math>bk|\varphi(n)</math> which means
  3 KB (542 words) - 17:45, 21 March 2023
• Geometric inequality
  ...[[area]] <math>A</math> and [[perimeter]] <math>P</math>, then <math>\frac{4\pi A}{P^2} \le 1</math>. This means that given a perimeter <math>P</math> f <b>Proof of Lemma: </b> Let <math>M</math> and <math>N</math> be the projections of <math>E</math> and <math>F</math> onto line <m
  7 KB (1,296 words) - 14:22, 22 October 2023
• Elementary symmetric sum
  ...f those numbers (<math>1 \leq k \leq n</math>). For example, if <math>n = 4</math>, and our set of numbers is <math>\{a, b, c, d\}</math>, then: ...um_{sym}f(x)</math>. The <math>n</math>th can be written <math>\sum_{sym}^{n}f(x)</math>
  2 KB (275 words) - 12:51, 26 July 2023
• Number theory/Advanced
  <cmath>f(z)=\sum_{n\ge 0}a_nq^n.</cmath> ...n series <math>G_4</math> and <math>G_6</math> are modular forms of weight 4 and 6 respectively.
  5 KB (849 words) - 16:14, 18 May 2021
• Divisibility rules
  ...nly if its units digit is divisible by 2, i.e. if the number ends in 0, 2, 4, 6 or 8. A number is divisible by <math>5^n</math> if and only if the last <math>n</math> digits are divisible by that power of 5.
  8 KB (1,315 words) - 18:18, 2 March 2024
• Induction
  ...it works for <math>n=1+1=2</math>, which in turn means it works for <math>n=2+1=3</math>, and so on. ...nd show that if <math>{n=k}</math> gives the desired result, so does <math>n=k+2</math>. If you wish, you can similarly induct over the powers of 2.
  5 KB (768 words) - 20:45, 1 September 2022
• Greatest common divisor
  <math>270=2\cdot3^3\cdot5</math> and <math>144=2^4\cdot3^2</math>. The common factors are 2 and <math>3^2</math>, so <math>GCD ...an use the recursive formula <math>GCD(a_1,\dots,a_n)=GCD(GCD(a_1,\dots,a_{n-1}),a_n)</math>.
  2 KB (288 words) - 22:40, 26 January 2021
• Overcounting
  "How many numbers less than or equal to 100 are divisible by 2 or 3 but not 4?". ...Suppose we know the total number of people invited to the party, say <math>n</math>.
  4 KB (635 words) - 12:19, 2 January 2022
• Constructive counting
  ...uare \square \square \square,</cmath> which we have to populate with <math>4</math> <math>A</math>s and <math>3</math> <math>B</math>s. Using constructi ...ath>B</math>s. Starting with the <math>A</math>s, we must choose the <math>4</math> boxes of their placement; because all the <math>A</math>s are indist
  12 KB (1,896 words) - 23:55, 27 December 2023
• Euclidean algorithm
  <math>r_{n-1} \pmod {r_n} \equiv 0</math><br> <math>r_{n-1} = r_n \cdot q_{n+1} +0</math><br>
  6 KB (924 words) - 21:50, 8 May 2022
• Generating function
  ...se 0}+{n \choose 1}x + {n \choose 2}x^2+\cdots+</math><math>{n \choose n}x^n</math>. ...s the number of ways we can get <math>{k}</math> heads when flipping <math>n</math> different coins.
  4 KB (659 words) - 12:54, 7 March 2022
• Binomial Theorem
  ...x]] <math>a</math>, <math>b</math>, and [[non-negative]] [[integer]] <math>n</math>, <center><math>(a+b)^n = \sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k</math></center>
  5 KB (935 words) - 13:11, 20 February 2024
• Prime number
  ...N = p_1p_2\cdots p_n + 1</math> is not divisible by any of them, but <math>N</math> must [[#Importance of Primes|have]] a prime factor, which leads to a ...ividing larger numbers would result in a quotient smaller than <math>\sqrt{n}</math>.
  6 KB (985 words) - 12:38, 25 February 2024
• Function
  ...in the second. For instance, one function may map 1 to 1, 2 to 4, 3 to 9, 4 to 16, and so on. This function has the rule that it takes its input value ...ve from <math>\mathbb{R} \rightarrow \mathbb{R}</math> (since <math>f(2) = 4 = f(-2)</math>) nor surjective from <math>\mathbb{R} \rightarrow \mathbb{R}
  10 KB (1,761 words) - 03:16, 12 May 2023
• Complementary counting
  ...ructive]] approach, the first digit can be one of seven integers; <math>1, 4, 5, 6, 7, 8,</math> and <math>9</math>. Note that the first digit cannot be ...use can be, four options for the second, and so on. Hence, there are <math>4^7 = 16384</math> ways she can color the four houses.
  8 KB (1,192 words) - 17:20, 16 June 2023
• Prime factorization
  ...the '''prime factorization''' of <math>n</math> is an expression for <math>n</math> as a product of powers of [[prime number]]s. An important theorem o <math>n = {p_1}^{e_1} \cdot {p_2}^{e_2}\cdot{p_3}^{e_3}\cdots{p_k}^{e_k}</math>
  3 KB (496 words) - 22:14, 5 January 2024
• Composite number
  ...me composite numbers are <math>4=2^2</math> and <math>12=2\times 6=3\times 4</math>. Composite numbers '''atleast have 2 distinct [[prime]] [[divisors]] 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 26 27 28 30 32 33 34 35 36 38 39 40
  6 KB (350 words) - 12:58, 26 September 2023
• Natural number
  ...tegers (sometimes called [[whole number]]s). In particular, <math>\mathbb{N}</math> usually includes zero in the contexts of [[set theory]] and [[abstr
  1 KB (162 words) - 21:44, 13 March 2022
• Ellipse
  ...ts are perpendicular. Drawing all four semi-axes divides the ellipse into 4 [[congruent (geometry)|congruent]] quarters. pair P=(3,12/5), F1=(-4,0), F2=(4,0);
  5 KB (892 words) - 21:52, 1 May 2021
• Base numbers
  ...46. This number can be rewritten as <math>2746_{10}=2\cdot10^3+7\cdot10^2+4\cdot10^1+6\cdot10^0.</math> ...</math>, spits out <math>P(n)</math>, the value of the polynomial at <math>n</math>. However, the oracle charges a fee for each such computation, so you
  4 KB (547 words) - 17:23, 30 December 2020

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)