Math Is Fun Forum

henryzz

Member

Registered: 2007-06-03

Posts: 14

Finding algebraic factors of (2^n)+-1

what are the methods for finding algebraic factors of (2^n)+-1

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,385

Re: Finding algebraic factors of (2^n)+-1

Do you mean prime factors?

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henryzz

Member

Registered: 2007-06-03

Posts: 14

Re: Finding algebraic factors of (2^n)+-1

no i mean like (2^2n)-1 = ((2^n)-1)*((2^n)+1)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Finding algebraic factors of (2^n)+-1

Remember that 2^n is just some number, so for 2^n + 1, you can't break it up into real factors.  2^n-1 however can easily be broken up as long as n is even since it is a difference of two squares.  If it's not even, then you can still do this but the term 2^n/2 will not be an integer, as is usually wanted when factoring.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

henryzz

Member

Registered: 2007-06-03

Posts: 14

Re: Finding algebraic factors of (2^n)+-1

what i want to know is there any more method of factoizing them

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Finding algebraic factors of (2^n)+-1

?