ON THE DISTRIBUTION OF INTEGERS REPRESENTABLE AS A SUM OF TWO $h$-TH POWERS
Saburô Uchiyama · Hokkaido Mathematical Journal · 1965
UCHIYAMAOur aim in this note is to present some elementary results conceming the distribution of integers which can be expressed as a sum of two h-th powers, where $h\geqq 2$ is a fixed integer.1.According to P. Erdos [2], R. P. Bambah and S. Chowla [1] have proved that for some suffi ciently large constant $C$ the interval $(n, n+Cn eq)$ always contains an integer of the form $x^{?}+y^{2},$ $n,$ $x$ and $y$ being integral, and Erd\"os [2] coniectures (among others) that this holds for every $C$ if $n\geqq n_{0}(C)$ .