How to SQL query posts IDs by categories AND authors?

Not the best solution 😛 but this could help you:

select 
    distinct(p.ID)
from
    wp_posts p,
    wp_term_relationships r,
    wp_term_taxonomy tt,
    wp_terms t
WHERE
    p.post_author in (1, 2, 3)
        and r.object_id = p.ID
        and tt.term_taxonomy_id = r.term_taxonomy_id
        and tt.taxonomy = 'category'
        and tt.term_id = t.term_id
        and t.term_id in (1, 2, 3);