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Prove by Induction. Prop: if the (greatest common factor) gcf(a,m) = f then there is k, l...

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Advance Math

Prove by Induction.

Prop: if the (greatest common factor) gcf(a,m) = f then there isk, l with ka + lm = f

Steps that we have already established is,

m = a(q1) + (r1)

a = (r1)(q2) + (r2)

(r1) = (r2)(q3) + (r3)

...

r(n-2) = r(n+1)q(n) + r(n)

r(n-1) = r(n)q(n+1) + 0 is the very last step to thissequence

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