Refinements of Lagrange's Four-Square Theorem. Issue 3 (16th March 2018) - Goldmakher, Leo; Pollack, Paul
Abstract: A well-known theorem of Lagrange asserts that every nonnegative integer n can be written in the form a 2 + b 2 + c 2 + d 2, where . We characterize the values assumed by a + b + c + d as we range over all such representations of n .