divisibility of cube numbers (cont.,)

Divisibility of cube numbers (cont.,)

When a³ is divided by (a+4),,the remainder will be 4(a-12),that is for all ‘a’ which are in multiples of 12 ,the remainder will be zero.

The general form correlating a³, the divisor (a+4),the quotient and the remainder is

  a³ = [8+ (a-2)² ] (a+4) + 4(a-12)

If the  divisor is (a+5),  it becomes,

a³ = [14 + (a-2)(a-3)] (a+5) + 5(a-20)

For the divisor (a+6),

a³ = [21 + (a-3)² ] (a+6) + 6(a-30)

for (a+7),

a³ = [ 30 + (a-3)(a-4)](a+7) + 7(a-42)