Resumen de A solution to weighted sums of squares as a square

Christopher S. Withers, Saralees Nadarajah

• 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.