Express the GCD(2546,122) as a linear combination of 2546 and 122
I found the gcd to be 8 and I went about writing it as a linear combination but somewhere I went wrong.. can someone find my mistake?
2=6-4(1)
2=6-[10-6(1)]
2=2(6)-10
2=2[16-10(1)]-10(1)
2=2(16)-3(10)
2=2(16)-3[106-16(6)]
2=14(16)-3(106)
2=14[122-106(1)]-3(106)]
2=14(122)-17(106)
2=14(122)-17[2546-122(20)]
2=354(122)-17(2546)
Obviously this is wrong because my linear combination doesn't equal 2. Where did I make a mistake?
