abstract algebra: for each pair of integers a and b below, find s,t ∈ Z such that gcd(a,b)=sa+tb?
for each pair of integers a and b below, find s,t ∈ Z such that gcd(a,b)=sa+tb
i) a=111 b=126
ii) a=89 b=144
iii) a=153 b=225
iv) a=1331 b=3113
v) a=12449 b=30031
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1)a= 111; b= 126
gcf(a,b)= 3
gcfsum(a,b)= 15*126-17*111
2)a= 89; b= 144
gcf(a,b)= 1
gcfsum(a,b)= 34*144-55*89
3)a= 153; b= 225
gcf(a,b)= 9
gcfsum(a,b)= 3*153-2*225
4)a= 1331; b= 3113
gcf(a,b)= 11
gcfsum(a,b)= 138*1331-59*3113
5)a= 12449; b= 30031
gcf(a,b)= 59
gcfsum(a,b)= 234*12449-97*30031