A solution to weighted sums of squares as a square

• Autores: Christopher S. Withers, Saralees Nadarajah
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 43, Nº. 8, 2012, págs. 1099-1108
• Idioma: inglés
• DOI: 10.1080/0020739x.2012.662290
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• Resumen

  • For n?=?1,?2,?�?, we give a solution (x1,?�?,?xn,?N) to the Diophantine integer equation . Our solution has Nof the form n!, in contrast to other solutions in the literature that are extensions of Euler's solution for N, a sum of squares. More generally, for given nand given integer weights m1,?m2,?�?,?mnwe give a solution to . The weights may be positive or negative and are subject to some restrictions. Choosing weights ±1 gives a solution to the problem of finding integer vectors of the same length.