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This is a linear Diophantine equation, related to Bézout's identity. + = + The smallest nontrivial solution in positive integers is 12 3 + 1 3 = 9 3 + 10 3 = 1729.It was famously given as an evident property of 1729, a taxicab number (also named Hardy–Ramanujan number) by Ramanujan to Hardy while meeting in 1917. [1]
Diophantus of Alexandria [1] (/ d aɪ oʊ ˈ f æ n t ə s /; [2] born c. AD 200 – c. 214; died c. AD 284 – c. 298) was a Greek mathematician, who was the author of two main works: On Polygonal Numbers, which survives incomplete, and the Arithmetica in thirteen books, most of it extant, made up of arithmetical problems that are solved through algebraic equations. [3]
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages.Numbers are written with combinations of letters from the Latin alphabet, each with a fixed integer value.
A Diophantine equation, in general, is one where the solutions are restricted to some algebraic system, typically integers. (In another usage ) Diophantine refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria, who made initial studies of integer Diophantine equations.
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values.
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
The general solution was found in 1880 by Carl Ernst August Amthor (1845–1916), headmaster of the Gymnasium zum Heiligen Kreuz (Gymnasium of the Holy Cross) in Dresden, Germany. [ 2 ] [ 3 ] [ 4 ] Using logarithmic tables , he calculated the first digits of the smallest solution, showing that it is about 7.76 × 10 206 544 cattle, far more ...
Roman numeral: LXX, lxx: Binary: 10001000101110000 2: Ternary: 10120000121 3: ... 73712 = number of n-Queens Problem solutions for n = 13; 73728 = 3-smooth number ...