divisibility of cube numbers (cont.,)

Divisibility of cube numbers (cont.,)

When a³ is divided by 4 ,for all even numbers the remainder is zero where as for odd numbers it is 1 for a in the form of (4n+1) and 3 for (4n-1).

When a³ is divided by (a+4)

1= 5(9) -44

8= 6(8) – 40

27 = 7(9) – 36

64= 8(12) – 32

125 = 9(17) – 28

216 = 10(24) – 24

343= 11(33) – 20

512 = 12(44) – 16

729 = 13(57)- 12

1000 = 14(72) – 8

 In  general it takes a form

a³ = [8+(a-2)²](a+4) + 4(a-12)