Working through a question i got to this stage where i need to:

Show that if m > n then ((a^2)^n) + 1 divides ((a^2)^m)− 1

Should i be looking to expand ((a^2)^n) + 1?

Printable View

- Nov 5th 2009, 01:05 PMsirellwoodShow that if m > n then ((a^2)^n) + 1 divides ((a^2)^m)− 1
Working through a question i got to this stage where i need to:

Show that if m > n then ((a^2)^n) + 1 divides ((a^2)^m)− 1

Should i be looking to expand ((a^2)^n) + 1? - Nov 5th 2009, 01:13 PMtonio
- Nov 5th 2009, 01:16 PMsirellwood
argh sorry. my bad. edited :-)

- Nov 7th 2009, 03:25 AMflyingsquirrel
- Nov 7th 2009, 03:37 AMMedia_ManExponents not Associative
Sirellwood:

The operator "^" is NOT associative, that is, a^(2^n) does not equal (a^2)^n in general -- in Latex,

Theorem: For

Proof: ...

Continue factoring the successive differences of squares k times until . QED

Your theorem is quite true, if rendered to the page in proper notation. (Thinking) - Nov 7th 2009, 03:38 AMtonio
- Nov 7th 2009, 03:45 AMtonio

I supposed that if the OP had wanted he could have writte a^(2^n) and not (a^2)^n, which means . OTOH, he could have simply written a^(2n) and thus I think you're right and he meant .

Even using simple ASCII one must be careful or even describe things by words when mathematical notation is cumbersome.

Tonio - Nov 7th 2009, 04:05 AMMedia_ManOn languageQuote:

one must be careful or even describe things by words when mathematical notation is cumbersome.