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Diophantine Equationseasy
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Bezout's Identity states that if aaa and bbb are integers with gcd⁡(a,b)=d\gcd(a, b) = dgcd(a,b)=d, then there exist integers xxx and yyy such that ax+by=dax + by = dax+by=d. For a=17a = 17a=17 and b=5b = 5b=5, we have gcd⁡(17,5)=1\gcd(17, 5) = 1gcd(17,5)=1. Which of the following pairs (x,y)(x, y)(x,y) is/are valid pairs of Bezout coefficients satisfying 17x+5y=117x + 5y = 117x+5y=1?