What can you conclude about gcd (a,b) if there are integers s,t with as + bt = 6
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What can you conclude about gcd (a,b) if there are integers s,t with as + bt = 6

[From: ] [author: ] [Date: 13-08-22] [Hit: ]
And if for some integers s and t, as+bt = q, then gcd(a,b) divides q (6 in this case).......
What can you conclude about gcd (a,b) if there are integers s,t with as + bt = 6?

Need some help here guys.

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That the gcd is a divisor of 6, i.e. gcd(a,b)=1,2,3 or 6.

The gcd(a,b) is the SMALLEST linear combination of a,b. i.e. the smallest positive integer such that there exist x,y such that ax+by = gcd(a,b). And if for some integers s and t, as+bt = q, then gcd(a,b) divides q (6 in this case).
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