On Waring's problem: two squares and three biquadrates

John B. Friedlander, Trevor D. Wooley

Published 2012-11-08, updated 2013-02-13Version 2

We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam Conjecture, we show that all large natural numbers n with 8 not dividing n, n not congruent to 2 modulo 3, and n not congruent to 14 modulo 16, are the sum of 2 squares and 3 biquadrates.