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?
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?
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.
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
Funny, if you read pre-twentieth century math books and proofs, they rarely rely on notation and speak almost solely in plain english words. "One more than an integer raised to a power of two must evenly divide one less than that same number raised any higher power of two..." Mathematical notation is a language unto itself that has extremely strict rules of grammar.one must be careful or even describe things by words when mathematical notation is cumbersome.