| 释义 |
Pellian, a. Math.|ˈpɛlɪən|
[f. the name of John Pell, an English mathematician (1610–85): see -ian.]
Applied to a particular kind of indeterminate equation: see quot. 1875. Also absol.
[1767Euler in Novi Commentarii Acad. Sci. Imp. Petropolitanæ XI. 28 (heading) De usu novi algorithmi in problemate Pelliano solvendo. Ibid. 31, pp = lqq + 1... Atque hoc est illud problema olim quidem maxime celebratum a solutionis ingeniosissimae auctore Pellianum vocatum.] 1862Rep. Brit. Assoc. Adv. Sci. 1861 i. 314 There does not seem to be any ground for attributing either the problem or its solution to Pell... Nevertheless the equation T2 - DU2 = 1 is often called the Pellian equation after him, probably upon Euler's authority. 1875Cayley Coll. Math. Papers IX. 477 The Pellian equation is y2 = ax2 + 1, a being a given integer number, which is not a square (or rather, if it be, the only solution is y = 1, x = 0), and x, y being numbers to be determined: what is required is the least values of x, y, since these, being known, all other values can be found. 1911Encycl. Brit. XIX. 853/1 This is usually called the Pellian equation, though it should properly be associated with Fermat, who first perceived its importance. 1974Sci. Amer. July 118/3 The Pellian for square hexes is 3x2 + 1 = y2, which is solved by finding the convergents of the continued fraction for the square root of 3. |