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KooBits (stylised as KooBits with capitalised K and B) designs and builds digital products for children and educators. KooBits was founded in 2016 by current CEO Stanley, with Professor Sam Ge Shuzhi and Dr Chen Xiangdong. [1] The trio saw an opportunity in the rapid growth of the ebook industry and decided to focus on creating software for ...
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Sum and Product Puzzle. The Sum and Product Puzzle, also known as the Impossible Puzzle because it seems to lack sufficient information for a solution, is a logic puzzle. It was first published in 1969 by Hans Freudenthal, [1] [2] and the name Impossible Puzzle was coined by Martin Gardner. [3] The puzzle is solvable, though not easily.
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. Waring's problem was proposed in 1770 by Edward ...
For this sequence, Abel's summation formula simplifies to. Similarly, for the sequence and for all , the formula becomes. Upon taking the limit as , we find. assuming that both terms on the right-hand side exist and are finite. Abel's summation formula can be generalized to the case where is only assumed to be continuous if the integral is ...
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Similar problems to Goldbach's conjecture exist in which primes are replaced by other particular sets of numbers, such as the squares: It was proven by Lagrange that every positive integer is the sum of four squares. See Waring's problem and the related Waring–Goldbach problem on sums of powers of primes.
The divisor summatory function is defined as. where. is the divisor function. The divisor function counts the number of ways that the integer n can be written as a product of two integers. More generally, one defines. where dk ( n) counts the number of ways that n can be written as a product of k numbers. This quantity can be visualized as the ...