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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  ∤  n   ,    n  ¬  ≡  2    (  mod    3  )    and    n  ¬  ≡  14    (  mod    16  )    are the sum of two squares and three biquadrates.

ON WARING'S PROBLEM: TWO SQUARES AND THREE BIQUADRATES