Question

Show that the cube of a positive integer is of the form 6q + r , where q is an integer and r=0,1,2,3,4,5.​


only answers

Answer 1

Let a be an arbitrary positive integer. Then, by Euclid’s division algorithm, corresponding to the positive integers ‘a’ and 6, there exist non-negative integers and r such that a = 6 q + r, where, 0 < r < 6

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Hence, the cube of a positive integer of the form 6q + r,q is an integer and r = 0,1,2, 3, 4,5 is also of the forms 6m, 6m + 1, 6m + 2, 6m + 3,6m + 4 and 6m + 5 i.e.,6m + r