Let E1 (N),N2 (N) and F3 (N) denote the numbers of natural numbers n neither exceeding N nor representing in the form x2 + y3 + z3 = n,x2 + y 3 +Z4= n and x2 + y3 + z 5 = n respectively. In 1937,H. Davenport and H. Heilbronn proved that.
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