detailed solution

6. Find the remainder when 15 + 25 + 35 + ... + 985 + 995 + 1005 is divided by 4. 7. Without performing actual division, determine whether 1 010 908 899 is divisible by 7, 11 and 13. 8. Find the solutions to the given system of linear congruence. x = 1 ( mod 3) x = 3 ( mod 5) x = 4 ( mod 7) 9. Solve the linear congruence 17x = 9 ( mod 276) using systems of congruence. 10. Solve the linear congruence x3 - 7x2 - 48x + 18 = 0 ( mod 54)