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Linear Combinations, Division and the Euclidean Algorithm

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Assume that d=sa+tb is a linear combination of integers a and b. Find infinitely many pairs of integers ( s sub k, t sub k ) with d=s sub k a + t sub k b

Hint: If 2s +3t =1, then 2 (s+3) + 3 (t-2) = 1

I would like a very detailed, as possible, explanation on how to work this problem if you please.

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Linear Combinations, Division and the Euclidean Algorithm are investigated.

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The pair of integers can be represented as (k1, k2), such that (s-k1)a + ...

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