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  • ...ss combined with the increasing need for navigational accuracy as European powers began colonizing other parts of the globe initiated a huge mathematical boo
    6 KB (846 words) - 20:30, 13 February 2025
  • ...ists of a sum of variables raised to [[nonnegative]], [[integer|integral]] powers and multiplied by [[coefficient]]s from a predetermined [[set]] (usually th
    6 KB (1,100 words) - 15:57, 30 August 2024
  • ==Differences and Sums of Powers== ...tric sequence]], it's easy to derive the general formula for difference of powers:
    3 KB (532 words) - 22:00, 13 January 2024
  • in the prime factorization of <math>n!</math>? We can find it as the sum of powers of <math>p</math> in all the factors <math>1,2,\dots, n</math>;
    10 KB (809 words) - 16:40, 17 March 2024
  • ...of prime power orders is unique. We can do this because if any two prime powers are not coprime then <math>k^{\times}</math> contains <math>C_{p^a}\times C
    15 KB (2,618 words) - 12:03, 19 February 2025
  • ...equations involving [https://en.wikipedia.org/wiki/Sums_of_powers sums of powers], combined with Vieta's formulas.
    2 KB (275 words) - 12:51, 26 July 2023
  • ** [[Sum and difference of powers]]
    2 KB (198 words) - 16:06, 7 December 2024
  • === Divisibility Rule for 2 and Powers of 2 === [[Divisibility rules/Rule for 2 and powers of 2 proof | Proof]]
    10 KB (1,572 words) - 22:11, 22 September 2024
  • ...o does <math>n=k+2</math>. If you wish, you can similarly induct over the powers of 2.
    5 KB (768 words) - 00:59, 29 September 2024
  • ...1}{a}, -\frac{1}{a} \right)</math> (if <math>a < 0</math>), generating the powers of <math>a</math> for any real <math>a</math>. The identity holds for all <
    4 KB (659 words) - 12:54, 7 March 2022
  • ...n''' of <math>n</math> is an expression for <math>n</math> as a product of powers of [[prime number]]s. An important theorem of [[number theory]] called the ...numbers, case by case. Use [[divisibility rules]] to check if primes (or powers of primes) are a factor and then move up to a different prime if said prime
    3 KB (496 words) - 22:14, 5 January 2024
  • ...ving.com/wiki/index.php/Sum_and_difference_of_powers Sum and difference of powers]
    2 KB (327 words) - 02:06, 28 April 2024
  • can be estimated from above and from below by the <math>n^th</math> powers of some constants strictly between <math>0</math> and <math>1</math>. Using
    8 KB (1,424 words) - 16:49, 17 February 2025
  • '''Logarithms''' are right inverses of powers. Logarithms, the [[right inverse]]s of powers can be written as <math>\log_a(b)</math> for some <math>a</math> and <math>
    5 KB (721 words) - 20:44, 9 March 2025
  • ...(r-1)</math>, and using the [[Sum and difference of powers | difference of powers]] factorization yields <cmath>S(r-1) = a_1(r-1)(1 + r + r^2 + \cdots + r^{n
    4 KB (649 words) - 21:09, 19 July 2024
  • ...y number that is a power greater than the second to be the sum of two like powers. ''I have discovered a truly marvelous demonstration of this proposition th
    3 KB (453 words) - 11:13, 9 June 2023
  • == Sum of Fourth Powers == ...are either <math> -1, 0 </math> or <math>1 \mod 5</math>. Thus, all fourth powers are either <math>0</math> or <math>1 \mod 5</math>.
    9 KB (1,434 words) - 01:15, 4 July 2024
  • ...than <math>\frac{1}{2}</math>. And we continue grouping the terms between powers of two. So we have
    2 KB (334 words) - 20:52, 13 March 2022
  • '''Sum of powers of divisors''': <math>\sigma_k(n) : = \sum_{d|n} d^k</math>; often <math>\t
    8 KB (1,410 words) - 09:32, 24 February 2025
  • We begin by writing down the first few powers of <math>7</math> mod <math>100</math>:
    16 KB (2,410 words) - 14:05, 3 January 2025

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