Question

use euclid's divison lemma to show that the cube of any positive is of the form any 9m+1 or 9m+8​

Answer 1

Heyaa☺

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Let m be any positive integer then 3p or 3p + 1 and 3p +2

Now,

we have to prove that the cube of each of these can be written in the form of 9q,9q + 1 and 9q+8

Now,

(3m)^3 = 27m^3=9(3m^3)=9q

where q = 3m^3

(3m + 1)^3 = 27m^3 + 27m^2 +9m + 1

=》9q + 1(where q = 3m^3 + 3m^2+m.

(3m + 2)^3 = 27m^3 + 54m^2+36m + 8

=》9q + 8 (where q = 3m^2 + 6m^2 + 4m.

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Hopw you understand..✌