Question

Why can't we use 2q+1 for show that cube of any positive integer is in the form 4q+1,4q

Answer 1

Step-by-step explanation:

a is a positive integer

using Euclid' s division lemma with a and b=4

a=4q+r, r=0,1,2,3.

If r=0

a=4q

a cube =64q cube =4 (4q)square =4q

=4q where q=4q cube

r=1

4q+1

a cube =4 (4q+1)cube

a cube =(4q)cube +3.4q square (1)+3.4q. 1sq+1 cube

=64q+48q+12q+1

=4 (4q cube +12q+3q)+1

a cube =4q+1,where q=4q +12q