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  2. Waring's problem - Wikipedia

    en.wikipedia.org/wiki/Waring's_problem

    In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers raised to the power k. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers.

  3. Polite number - Wikipedia

    en.wikipedia.org/wiki/Polite_number

    A Young diagram representing visually a polite expansion 15 = 4 + 5 + 6. In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers.

  4. Landau's problems - Wikipedia

    en.wikipedia.org/wiki/Landau's_problems

    Landau's fourth problem asked whether there are infinitely many primes which are of the form = + for integer n. (The list of known primes of this form is A002496 .) The existence of infinitely many such primes would follow as a consequence of other number-theoretic conjectures such as the Bunyakovsky conjecture and Bateman–Horn conjecture .

  5. Sums of three cubes - Wikipedia

    en.wikipedia.org/wiki/Sums_of_three_cubes

    Semi-log plot of solutions of + + = for integer , , and , and .Green bands denote values of proven not to have a solution.. In the mathematics of sums of powers, it is an open problem to characterize the numbers that can be expressed as a sum of three cubes of integers, allowing both positive and negative cubes in the sum.

  6. 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.

  7. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Lander, Parkin, and Selfridge conjecture: if the sum of -th powers of positive integers is equal to a different sum of -th powers of positive integers, then +. Lemoine's conjecture : all odd integers greater than 5 {\displaystyle 5} can be represented as the sum of an odd prime number and an even semiprime .

  8. Subset sum problem - Wikipedia

    en.wikipedia.org/wiki/Subset_sum_problem

    The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . [ 1 ]

  9. Sum of four cubes problem - Wikipedia

    en.wikipedia.org/wiki/Sum_of_four_cubes_problem

    The sum of four cubes problem [1] asks whether every integer is the sum of four cubes of integers. It is conjectured the answer is affirmative, but this conjecture has been neither proven nor disproven. [2] Some of the cubes may be negative numbers, in contrast to Waring's problem on sums of cubes, where they are required to be positive.