I have a question that involves two parts. I believe I have the first part correct. The second part is what I am confused on and explain below.
a) Find the gcd(260,154)
260 = 1(154) + 106
154 = 1(106) + 48
106 = 2(48) +10
48 = 4(10) + 8
10 = 1(8) + 2
8 = 4(2) + 0
Thus the gcd(260,154) is 2 since it is the last non-zero remainder.
***b) Find integers such that 154x + 260y = 4
Well, usually I would use part a and find the line with 4 as a remainder and work backwards until I find x and y. My problem is that I don’t have 4 as a remainder in any of the lines above and therefore I am not sure what to do? I may have calculated the gcd incorrectly, but I have checked it several times and get the same answer. Also, my book examples find x and y differently than the way I am being taught. Any suggestions? Thanks!