Maths question

RedRebel92

i got this in my mocks: prove by induction that 3 is a factor of 4(to the power of n) - 1. can anyone help me??

partyatmygaff

I can't help you as I haven't done any of that yet but if you want a better way of typing out maths on boards.ie just use the latex tags.

[LATEX]Prove[/LATEX][LATEX]by[/LATEX][LATEX]induction[/LATEX] [LATEX]that[/LATEX] [LATEX]3[/LATEX] [LATEX]is[/LATEX] [LATEX] a[/LATEX] [LATEX]factor[/LATEX] [LATEX]of[/LATEX] [LATEX]4^n^-1[/LATEX]



The tag is LATEX /LATEX with square brackets around both.

mark.oc

RedRebel92 wrote: »

i got this in my mocks: prove by induction that 3 is a factor of 4(to the power of n) - 1. can anyone help me??

Skipping the prove true for n=1 section:

Assume true for n=k:
4^k - 1 = 3A
4^k = 3A + 1

Prove true for n=k+1:
4^(k+1) - 1
(4^k x 4^1) - 1
(3A + 1)x4 - 1 (from step 1)
12A + 4 - 1
12A + 3
which is divisible by 3.

partyatmygaff

mark.oc wrote: »

Skipping the prove true for n=1 section:

Assume true for n=k:
[LATEX]4^k - 1 = 3A[/LATEX]
[LATEX]4^k = 3A + 1[/LATEX]

Prove true for n=k+1:
[LATEX]4^(k+1) - 1[/LATEX]
[LATEX](4^k x 4^1) - 1[/LATEX]
[LATEX](3A + 1)*4 - 1 [/LATEX](from step 1)
[LATEX]12A + 4 - 1[/LATEX]
[LATEX]12A + 3[/LATEX]
which is divisible by 3.

Added latex tags to make it easier to read. Hope you don't mind.

Reillyman

Testing:

[LATEX] x^2+3x+15=7^(n-1) = 2^k [/LATEX]