On the problem of large gcd for disjoint residue classes

Jan Fornal, Yu-Chen Sun

Consider $k$ pairwise disjoint residue classes $a_i(\mathrm{mod}{m}_i)$. We prove that \[ \max_{1\leq i<j\leq k}\gcd(m_i,m_j) \gg k\exp\!\left(-(2+o(1)) \sqrt{\frac{\log k}{\log\log k}}\ri…