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  2. Sums of powers - Wikipedia

    en.wikipedia.org/wiki/Sums_of_powers

    In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.

  3. Euler's sum of powers conjecture - Wikipedia

    en.wikipedia.org/wiki/Euler's_sum_of_powers...

    Jaroslaw Wroblewski, Equal Sums of Like Powers; Ed Pegg Jr., Math Games, Power Sums; James Waldby, A Table of Fifth Powers equal to a Fifth Power (2009) R. Gerbicz, J.-C. Meyrignac, U. Beckert, All solutions of the Diophantine equation a 6 + b 6 = c 6 + d 6 + e 6 + f 6 + g 6 for a,b,c,d,e,f,g < 250000 found with a distributed Boinc project

  4. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    1 Sums of powers. 2 Power series. Toggle Power series subsection. 2.1 Low-order polylogarithms. 2.2 Exponential function. ... Sum of reciprocal of factorials

  5. Polynomial expansion - Wikipedia

    en.wikipedia.org/wiki/Polynomial_expansion

    In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...

  6. Lander, Parkin, and Selfridge conjecture - Wikipedia

    en.wikipedia.org/wiki/Lander,_Parkin,_and_Self...

    Extending the number of terms on either or both sides, and allowing for higher powers than 2, led to Leonhard Euler to propose in 1769 that for all integers n and k greater than 1, if the sum of n k th powers of positive integers is itself a k th power, then n is greater than or equal to k.

  7. Binomial theorem - Wikipedia

    en.wikipedia.org/wiki/Binomial_theorem

    In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power ⁠ (+) ⁠ expands into a polynomial with terms of the form ⁠ ⁠, where the exponents ⁠ ⁠ and ⁠ ⁠ are nonnegative integers satisfying ⁠ + = ⁠ and the coefficient ⁠ ⁠ of each term is a specific positive integer ...

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  9. Faulhaber's formula - Wikipedia

    en.wikipedia.org/wiki/Faulhaber's_formula

    Since a = n(n + 1)/2, these formulae show that for an odd power (greater than 1), the sum is a polynomial in n having factors n 2 and (n + 1) 2, while for an even power the polynomial has factors n, n + 1/2 and n + 1.

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