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

Posted by Aniket Jariwala 5 years ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years ago

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

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.

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CBSE > Class 10 > Mathematics