Question

show that the cube on any positive integer is either in the form of 4m. 4m+1, 4m+ 3 for any integer m

Answer 1

A positive integer is 4
It's cube is 64
it can also be written as 4 x ( 16 )
I.e. 4 x ( m ).

Another positive integer is 2
It's cube 8
it can also be written as 4 x ( 2 ) + 1
I.e. 4 x ( m ) + 1

Similarly another positive integer is 3
It's cube is 27
it can also be written as 4 x ( 6 ) + 3
I.e. 4 x ( m ) +3