Problem of the Week

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Sums of Multiples Squares

Posted: January 1, 2024

36 % of users got this correct

According to a result of John Conway, every positive integer can be written in the form (a²)+ 2(b²) + 3(c²) + 4(d²) where a, b, c, d are nonnegative integers. Often there are multiple choices for a, b, c, d and a, b, c, and d are not necessarily different values. Find the choices for a, b, c, d as a 4-digit number abcd where 1(a²)+ 2(b²) + 3(c²) + 4(d²) = 98 and (a)(b)(c)(d) is a maximum.

Problem submitted by Pat Costello, Eastern Kentucky University