If 3731s + 6149t = 13 then 3731(2s) + 6149(2t) =26.
Hi everyone!
I have the following problem:
Which of these equations have an integer solution:
3731s + 6149t = 26
1001s + 2261t = 1
495s + 1704t = 1
385s + 17081t = 1
I thought the first one would not have an integer solution because 26 is not the gcd of 3731 and 6149, but 13 is. So I thought that it does not have an integer solution because if it did the equation would have to be 3731s + 6149t = 13, but according to the answer key it does have an integer solution. Could anyone explain why?
Thank you everyone!