The site's wording does not say whether a factor may repeat within a product, and the two readings have different answers on the record: when repetitions are allowed the condition on $A$ is stronger, and [ERS73] answers both questions no (see Formulation); when the factors of each product are distinct the condition is weaker, and the site's commentary calls both questions open. The site's commentary itself calls the original sources ambiguous on this point. The change inserts "(where each product runs over a subset of $A$)" after "$a_i,b_j\in A$", in the words of Erdős's definition of property $P$ in [Er80], printed p. 114: "(where each product runs over a subset of the $a$'s)". That is the poser's own statement of both questions, and it fixes the distinct-factor reading; the two subsets may overlap, since no disjointness is required there. The poser's other texts are silent but agree with it: [Er65], printed p. 182, introduces the condition (4), $\prod_{r=1}^{l_1}a_{i_r}=\prod_{r=1}^{l_2}a_{j_r}$ only if $l_1=l_2$, as the alternative to the distinct-products condition (3), whose products are over subsets ($\epsilon_i=0$ or $1$), [Er69], printed p. 81, display (12), writes $\prod_{r=1}^{q_1}a_{i_r}=\prod_{r=1}^{q_2}a_{j_r}$ only if $q_1=q_2$, and [Er73], printed p. 132, writes the products as $a_{i_1}\cdots a_{i_r}=a_{j_1}\cdots a_{j_s}$, neither saying whether the indices repeat. The silence is therefore already in the poser's earlier texts, and no text of his fixes the repetitions-allowed reading. The results about that reading are credited, not counted: Theorems 2 and 6 of Erdős, Ruzsa and Sárközy [ERS73], with the transfer to product sets that the site's commentary gives, and Tao's sharp constant from Granville and Soundararajan [GrSo01] in forum post 4061 (2 February 2026), all recorded under Formulation and Known Results.