Infinite sets of b-additive and b-multiplicative Ramanujan-Hardy numbers

Let b be a numeration base. A b-additive Ramanujan-Hardy number N is an integer for which there exists at least an integer M, called additive multiplier, such that the product of M and the sum of base b digits of N, added to the reversal of the product, gives N. We show that for any b there exists an infinity of b-additive Ramanujan-Hardy numbers and an infinity of additive multipliers. A b-multiplicative Ramanujan-Hardy number N is an integer for which there exists at least an integer M, called multiplicative multiplier, such that the product of M and the sum of base b digits of N, multiplied by the reversal of the product, gives N. We show that for an even b, b≡ 1 3, and for $b=2$, there exists an infinity of b-multiplicative Ramanujan-Hardy numbers and an infinity of multiplicative multipliers. These results completely answer two questions and partially answer two other questions among those asked in V. Niţică, About some relatives of the taxicab number, arXiv:1805.10739v4.