I'm taking an abstract algebra class. I have a question in which I am given two systems of linear congruences. I am given the solution to each system and asked to confirm the solutions using the Chinese Remainder Theorem. However, in both cases, my systems contain non-prime mod values...so, I'm not sure how I am supposed to use the Chinese Remainder Theorem to confirm the solutions. One of the systems is: x = 1 mod 8 and x = 5 mod 10. The solution given is x = 25 mod 40. How do I confirm the answers using the Chinese Remainder Theorem? I see that GCD(8, 10) = 2...and that 2 divides (5-1 =4). I'm just not sure how to proceed, since all the examples in my text involved the Chinese Remainder Theorem. Thoughts?