Problem of the Week 1040

A Special Sum of Squares

Find 7 (not necessarily distinct) positive integers, at least one of which is greater than 1040, such that the sum of their squares is 7 times the product (of the 7 integers).

Extra Credit: Solve this with 31 instead of 7 in all places.

Source: Gerald Heuer, Concordia College.

© Copyright 2005 Stan Wagon. Reproduced with permission.