Question

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

Answer 1

Answer:

Step-by-step explanation:

let a be any positive integer we apply the division lemma, with a and b is equal to 30 greater are greater 3 the possible repair under r0 1 and 2 that is they can be 3q or 3q + 1 or 3q + 2 where q is quotient

Now (3q')³=9q'³ which can be written in the form of 9m since 9 is is divisible by 9.

Again (3q'+1)³=27q³+27q'²+9q'+1

=9(3q'³+3q³+q')+1

Which can be written in form 9M + 1 since 9(3q'³+3q'²+q') is divisible by 9

Lastly,

(3q'+2)³=27q³ +54q'²+36q'+8

=9(3q'³+6q'²+4q')+8

Which can be written in form of 9 m + 8 since 27q + 54 q square + 36 q i.e. 9(3q³+6q'²+4q')+8 is divisible by 9 therefore , cube of any positive integer is of the form of of 9m, 9m + 1 or 9m + 8

Answer 2

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