Claims

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1934_12_01_romanoff: Satz II of Romanoff's 1934 paper: for each fixed integer a at least 2, every interval (0, x) holds more than a fixed positive proportion of integers of the form p + a^n, so Problem 244 has a yes for every integer C; refereed.

2025_03_17_ding: Theorem 1.1 of Ding's arXiv paper gives positive lower density for almost every real C > 1, and Theorem 1.2 of its fifth version gives it for the golden ratio, a specified base; a preprint with no journal record, claimed.

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