## use Euclid’s division lemma to show that the cube of any positive integer is of the form 9 m , 9 m + 1 or 9 m + 8 .

Question

use Euclid’s division lemma to show that the cube of any positive integer is of the form 9 m , 9 m + 1 or 9 m + 8 .

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2 weeks 2021-11-19T16:12:19+00:00 2 Answers 0 views 0

Step-by-step explanation:

we know that

euclids division lemma a=bq+r,0 is less than or equal to r is<b

let a be the cube of amy positive integer

b=9

0is less than are equal to r<b

the reminders are 0,1,2,3,4,5,6,7,8

a=9m+0

a=9m+1

a=9m+2

a=9m+3

a=9m+4

a=9m+5

a=9m+6

a=9m+7

a=9m+8

here ask cube of any positive integer

so, 9m,9m+1,9m+8

hence proved