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Oct
17
comment Cycle Length of the Positive Powers of Two Mod Powers of Ten
So if M is a number which leaves a residue of 1 mod 5^k, and a residue of 0 mod 2^k, what residue does it leave mod 10^k?
Oct
16
comment Exhibit an explicit bijection between irreducible polynomials over finite fields and Lyndon words.
A tiny bit of additional evidence (still not conclusive): springerlink.com/index/P6X9P2BV73L2X2GG.pdf "As there exists a bijection between Lyndon words over an alphabet of cardinality k and irreducible polynomials over Fk [10]..." where the reference [10] is to Golomb's paper.
Oct
16
answered Exhibit an explicit bijection between irreducible polynomials over finite fields and Lyndon words.
Oct
16
awarded  Critic
Oct
16
answered What do models where the CH is false look like?
Oct
15
comment Two finite groups with the same identical relations?
<bangs head on keyboard> of course. I need to think about what my question really ought to be.
Oct
15
comment Two finite groups with the same identical relations?
Er... no, why? Of course any two finite groups are quotients of the same free group if you choose it to have enough generators. Oh, I think I see what you're confused by: identical relations aren't the same thing as "relations" as in "generators and relations". Those are not relations satisfied by particular generators, but rather relations that are satisfied by all the elements of the group.
Oct
15
answered Can one make Erdős's Ramsey lower bound explicit?
Oct
15
awarded  Scholar
Oct
15
comment Two finite groups with the same identical relations?
Of course - thanks. How about if the order of the group is fixed? If G and H are non-isomorphic of the same order, can they still have the same identical relations? Thanks again - if nobody notices the comment I'll post this as a separate question.
Oct
15
accepted Two finite groups with the same identical relations?
Oct
15
awarded  Student
Oct
15
asked Two finite groups with the same identical relations?
Oct
15
answered Reading for finite Fourier Analysis
Oct
15
answered Does finite math need the Axiom of Infinity?
Oct
15
comment Does finite math need the Axiom of Infinity?
"maybe you could do it without" - I don't think you can. Goodstein's Theorem cannot be proved in PA, and I'm quite sure it cannot be proved in ZFC minus the axiom of infinity either.
Oct
15
awarded  Editor
Oct
15
comment Linear transformation that preserves the determinant
Of course - just missed that. It may actually make the claim easier to prove, I'm not sure.
Oct
15
revised Linear transformation that preserves the determinant
added 88 characters in body
Oct
14
answered Linear transformation that preserves the determinant