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A typical Diophantine problem is to find two integers x and y such that their sum, and the sum of their squares, equal two given numbers A and B, respectively: = + = +. Diophantus's major work is the Arithmetica, of which only a portion has survived. [23]
Math and Other Problems is the first album released by Atlanta-based rock band Marvelous 3. The album was released in 1997 through the Deep South label. Track listing. All songs written by Butch Walker. "Appetite" - 2:57 "Make Up" - 3:00 "Last Sleep" - 3:07 "Leopard Print" - 3:08 "Retail Girl" - 3:27 "Pizza and Wine" - 3:35 "Cars Collide" - 3:59
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See Waring's problem and the related Waring–Goldbach problem on sums of powers of primes. Hardy and Littlewood listed as their Conjecture I: "Every large odd number (n > 5) is the sum of a prime and the double of a prime". [31] This conjecture is known as Lemoine's conjecture and is also called Levy's conjecture.
The exception occurs when the original number has a digital root of 9, whose digit sum is itself, and therefore will not be cast out by taking further digit sums. The number 12565, for instance, has digit sum 1+2+5+6+5 = 19, which, in turn, has digit sum 1+9=10, which, in its turn has digit sum 1+0=1, a single-digit number.
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 ]
In mathematics, a Kloosterman sum is a particular kind of exponential sum.They are named for the Dutch mathematician Hendrik Kloosterman, who introduced them in 1926 [1] when he adapted the Hardy–Littlewood circle method to tackle a problem involving positive definite diagonal quadratic forms in four variables, strengthening his 1924 dissertation research on five or more variables.
The value of () can be given by several series. In terms of a sum involving the floor function it can be expressed as: [5] = + = (⌊ + ⌋ ⌊ + ⌋).This is a consequence of Jacobi's two-square theorem, which follows almost immediately from the Jacobi triple product.
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