We report here on the computational verification of Zhi-Wei Sun's “1-3-5 conjecture” for all natural numbers up to $105103560126$. This, together with a result of two of the authors, completes the proof of that conjecture. Furthermore the computations made in the verification process of the 1-3-5 conjecture revealed a refinement of it, which we state as a separate conjecture at the end of the paper.

中文翻译：

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孙志伟的1-3-5猜想及其改进报告

我们在此报告孙志伟的“ 1-3-5猜想”对所有自然数直至 $105103560126$。这与两位作者的结果一起，证明了这一推测。此外，在1-3-5猜想的验证过程中进行的计算显示出它的改进，在本文结尾处我们将其表示为单独的猜想。