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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.
In computational complexity theory, the 3SUM problem asks if a given set of real numbers contains three elements that sum to zero. A generalized version, k-SUM, asks the same question on k elements, rather than simply 3. 3SUM can be easily solved in () time, and matching (⌈ / ⌉) lower bounds are known in some specialized models of computation (Erickson 1999).
The problem is rather easily solved once the concepts and perspectives are made clear. There are three parties involved, S, P, and O. S knows the sum X+Y, P knows the product X·Y, and the observer O knows nothing more than the original problem statement. All three parties keep the same information but interpret it differently.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Subset sum problem, an algorithmic problem that can be used to find the shortest representation of a given number as a sum of powers; Pollock's conjectures; Sums of three cubes, discusses what numbers are the sum of three not necessarily positive cubes; Sums of four cubes problem, discusses whether every integer is the sum of four cubes of integers
In elementary algebra, factoring a polynomial reduces the problem of finding its roots to finding the roots of the factors. Polynomials with coefficients in the integers or in a field possess the unique factorization property, a version of the fundamental theorem of arithmetic with prime numbers replaced by irreducible polynomials.
Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. [2] The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows two columns of three apples and two apples ...
Euler's factorization method is a technique for factoring a number by writing it as a sum of two squares in two different ways. For example the number 1000009 {\displaystyle 1000009} can be written as 1000 2 + 3 2 {\displaystyle 1000^{2}+3^{2}} or as 972 2 + 235 2 {\displaystyle 972^{2}+235^{2}} and Euler's method gives the factorization ...