show that cube of any positive integer is of the form 4m,4m+1 or 4m+8,for some integer m.

show that cube of any positive integer is of the form 4m,4m+1 or 4m+8,

1.	show that cube of any positive integer is of the form 4m,4m+1 or 4m+8,for some integer m.
Answer» a=bq×rA=4q×r (where q is any poistive no.) 0<=r>4r=0,1,2,3Put r in a=bq+r(4q+0)cube=64q^3=4(16q^3)=4m(m=16q^3)(4q+1)cubeDo like (4q+0)cube