2.31. Show that for each of the following values of a and b, there exists x,...

2.31. Show that for each of the following values of a and b, there exists x, y in Z satisfying ax + by = 11. (i) a = 11, b = 0, (ii) a = 22, b = 11, (iii) a = 33, b = 22, (iv) a = 451, b = 33, (v) a = 484, b = 451.

2.39. Prove that gcd(ad, bd) = |d|gcd(a, b).

2.44. Does the Diophantine equation 12x + 33y = 1 have an integer solution? If so, can you list all integer solutions?

2.47. For nonzero integers a, b, c, gcd(a, b, , c) denotes the largest integer that divides all of them. Show that gcd(a, b, c) = gcd(a, gcd(b, c)).

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Colby Messinger answered 6 months ago

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