I'm writing my thesis in math and I want to include this theorem by Erdos (article linked below). I'm trying to figure out the proof of theorem 3 (on page 6). In equation (30) he states that $M_k≤N_k2^{−2^{k−1}}$ which I'm certain is wrong. $M_k$ is the product of all $m_i$'s from 1 to $k$ and $N_k$ is the least common multiple so in any case $M_k\geq N_k$. Later on he uses it to finish up his proof. If anyone can figure out how to modify the proof so that it is sound, or give me some idea how to, I would be very grateful. (sorry if the formatting and the language is bad. I'm new to this)
Here is the link to the article: https://users.renyi.hu/~p_erdos/1976-44.pdf
It looks wrong to me too. It should be the other way round:
$$N_k\le M_k\cdot2^{-2^{k-1}}$$
which appears to make the step on page 7 irrelevant.