number Theory questions

Problem 4. (5 points) A Diophantine equation is any equation involving integers, variables, and ele- mentary operations of addition, subtraction and multiplication. Given a Diophantine equation E we can replace the equal sign " = " by " = " mod m to get a congruence mod m. For the purposes of this problem we will call this congruence E mod m. (1) True or False? Justify :If a Diophantine equation E has an integer solution then E mod m has a solution for every m. (2) True or False? Justify :If a Diophantine congruence E mod M has a solution for all m then E has an integer solutions