Let {m1,m2,…} be a (finite or infinite) set of positive integers. Consider the system of congruences
(1) x\equiv 2m_i^2 \pmod{2m_i\minus{}1} ( i\equal{}1,2,... ).
Give a necessary and sufficient condition for the system (1) to be solvable. modular arithmeticnumber theory proposednumber theory