Let a and b be positive integers.
* use the euclidean algorithm to compute the following greatest common divisor: gcd(139024789,93278890)
* then, use the extended euclidean algorithm to find integers u and v such that au + bv = gcd(a, b) for the same gcd(a, b) values as above.
* finally, suppose that there are integers u and v satisfying au + bv = 6. is it necessarily true that gcd(a, b) = 6? if not, give a specific counterexample, and describe in general all of the possible values of gcd(a, b).