An astronomer is making measurements with his telescope when he notices that his vision field is off by x micronanometers (which we will assume is a measurement that exists) to the right. His telescope can only be moved to the right or to the left, however, and only via his automated, highly-calibrated machinery by certain predetermined fixed integer amounts. If, for example, one of these amounts is 7 micronanometers, then he can move his vision field by any multiple of 7 micronanometers to the left or right. Given a value of x and a set {m1, m2, . . . , mn} of predetermined fixed movement amounts, your job will be to advise the astronomer as to which of the movements to choose. Required:
How many times the movement should be applied, and the direction of the movement so that he can make his field of vision perfect?