Posted: Wed Oct 20, 2004 3:19 pm    Post subject: A proof

Let be positive integers with greatest common divisor .
Show that there exists a positive integer such that implies there exist nonnegative integers such that .

Posted: Wed Oct 20, 2004 11:09 pm    Post subject:

By Euclidean Algorithm, we can ensure a linear combination, perhaps with negative coefficients.

For sufficient large , there must be a very large coefficient in each of its linear combination. Using the identity , we can reduce the large coefficient a bit and increase other coefficients until they are non-negative.

Please work it out in a concrete way._________________

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