Can someone please explain this solution (1 Viewer)

[vds700]

2003 HSC Q8a)Suppose that w^3 = 1 and w=/ 1 and k is a positive integer
(i)Find the 2 possible values of
1 + w^k + w^(2k)

I don't understand in the solution where it says let k = 3m + r and r = 0, 1 or 2 (that is r = kmod3) What does kmod 3 mean?

If someone could please expalin this, it'd be great.

 

[jkwii]

ok to make it easy to understand. k is either
a) divisible by 3
b) not divisible by 3

so we take 3 substitutions:
k = 3a
k = 3a + 1
k = 3a + 2

substiuting them into 1 + w + w^2 = 0 will give you the correct answer of:

if k = 3a, 1 + w + w^2 = 3
if k = 3a +1, 3a +2, 1 + w + w^2 = 0

i think. try it again.

 

[samwell]

Yep u r rite. Its to make k either divisible by 3 or not divisinbe by three. siince we already noe that w^3=1 and 1+w+w^2=0
finding solutions of 1+w^k+w^2k is made possible by making the either divisble or not divisble by 3.

 

[vds700]

ok to make it easy to understand. k is either
a) divisible by 3
b) not divisible by 3

so we take 3 substitutions:
k = 3a
k = 3a + 1
k = 3a + 2

substiuting them into 1 + w + w^2 = 0 will give you the correct answer of:

if k = 3a, 1 + w + w^2 = 3
if k = 3a +1, 3a +2, 1 + w + w^2 = 0

i think. try it again.

Makes sense now. Thankyou