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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 (866 words) - 06:57, 17 January 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) - 14:57, 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) - 21:00, 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) - 15:40, 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
    16 KB (2,660 words) - 22:42, 28 August 2024
  • ...equations involving [https://en.wikipedia.org/wiki/Sums_of_powers sums of powers], combined with Vieta's formulas.
    2 KB (275 words) - 11:51, 26 July 2023
  • ** [[Sum and difference of powers]]
    2 KB (198 words) - 15:06, 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) - 21:11, 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) - 23:59, 28 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) - 11:54, 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) - 21:14, 5 January 2024
  • ...ving.com/wiki/index.php/Sum_and_difference_of_powers Sum and difference of powers]
    2 KB (327 words) - 01:06, 28 April 2024
  • can be estimated from above and from below by the <math>n</math>-th powers of some constants strictly between <math>0</math> and <math>1</math>. Using
    8 KB (1,469 words) - 20:11, 16 September 2022
  • ...(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) - 20:09, 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) - 10:13, 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) - 00:15, 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) - 19:52, 13 March 2022
  • '''Sum of powers of divisors''': <math>\sigma_k(n) : = \sum_{d|n} d^k</math>; often <math>\t
    8 KB (1,401 words) - 16:49, 10 January 2025
  • We begin by writing down the first few powers of <math>7</math> mod <math>100</math>:
    16 KB (2,410 words) - 13:05, 3 January 2025
  • Aha! We see powers of two in each of our terms! Therefore, we can say that ...did not consider powers of two yet(since our interval was strictly between powers of 2), so we have to add <math>\sum_{k=1}^{n}{2^k}</math>.
    10 KB (1,702 words) - 21:23, 25 July 2024

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