Question

show that 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 form 6m+r

Answer 1

let a be any +ve integer
b=6

by euclid 's division lemma,

a=bq+r, 0=< r < b
a= 6q+r,0=< r

when

r=0,a = 6q= (6q)3 ---> a3 = 216q3 =6(36q3)=6q(where m is = 6q3 )

by similar manner u can prove for

r=1,2,3,4,5

and u will get the proof

Answer 2

Answer:

hey mate here's your answer

see attachment^_^