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41. Suppose a is a number >1 with the following property: for all b, c, if...

41. Suppose a is a number >1 with the following property: for all b, c, if a divides bc and a does not divide b, then a divides c. Show that a must be prime.

44. Prove that for all numbers a, b, m, if (a, m) = 1 and (b, m) = 1, then (ab, m) = 1.

46. Prove that for all numbers a, b, if d = (a, b) and ra + sb = d, then (r, s) = 1.

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