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?

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- November 5th 2009, 02:05 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? - November 5th 2009, 02:13 PMtonio
- November 5th 2009, 02:16 PMsirellwood
argh sorry. my bad. edited :-)

- November 7th 2009, 04:25 AMflyingsquirrel
- November 7th 2009, 04:37 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) - November 7th 2009, 04:38 AMtonio
- November 7th 2009, 04:45 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 - November 7th 2009, 05:05 AMMedia_ManOn languageQuote:

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