Math

A Reformulation of Z-Reg.2
Theory A is the set of all sentences(entailed from FOL with identity and membership) by the following non logical axioms: (1) Comprehension: for n=0,1,2,3,...; if phi(y,w1,...,wn) is a formula in which y,w1,...,1n *are* its sole free variables and in which x is not free,then Aw1...wn Ar As E!x Ay ( y e x <-> ... 18 Jun 2010 17:59

24 is gorgeous
Take the coprimes of 24 {1,5,7,11,13,17,19,23} and divide them into 24 to get {0,4,3,2,11,7,5,1} with sum 33. Find the remainders of the squares of these numbers when divided by 24 to get {1,4,9,16,1,1,1} also with the same sum of 33. How often does this happen? ... 15 Jun 2010 20:57

Consecutive numbers and representation as sum of two squares
Hi, I need to prove that there is no 4 consecutive natural numbers such that each of them is sum of two squares. Can you give me some hint ? Thanks. ... 16 Jun 2010 04:32

16 is gorgeous
Take the coprimes of 16 and divide them into 16. You get 0,1,1,2,7,5,3,1 with sum 20. Take all the squares of the coprimes {1,3,5,7,9,11,13,15} and find the sum of the remainders when divided by 16. You get 1,9,9,1,1,9,9,1 with sum 40. The above 20 divides this 40. (a)Does this happen with other powers of 2?... 15 Jun 2010 20:57

Quick Question
What's the highest degree polynomial for which all roots can be written in terms of known functions? TIA. ... 17 Jun 2010 15:39

Divisibility of polynomials of several variables
Will divide the polynomial (1-x^i y^j z^k) by the polynomial (1-x z) (1-yz^m) exactly with no remainder for some set of natural numbers i,j,k,m>=0? If yes, find such a value of i,j,k,m. ... 16 Jun 2010 02:23

heavy water in comets is already proof Re: Additive Creation; Dirac's new radioactivities Chapt 5 #169; ATOM TOTALITY
Archimedes Plutonium wrote: Now I am wondering if there is a chemical element, say francium, or say a radioactive isotope that we can track if there was a single atom of that element? An element that is very easy to monitor and track if there was a singular atom of it in an experiment. I und... 15 Jun 2010 16:32

fundamental representations
Hi folks - I have a couple of basic questions about fundamental representations. First of all, does every group have a set of fundamental representations, or just the semi-simple groups? Secondly, I know that in the case of the (compact?) semi-simple groups, any other representation of the group can be constr... 15 Jun 2010 19:52

history of sciences and deciding-evidence Chapt 2 #167; ATOM TOTALITY
I am sort of glad I took that journey down the road of the history of physics or the history of science for it made better my desire to organize this book and to make me aware of how important Dirac's new radioactivities is to this theory of Atom Totality. I could read Darwin's book "On the Origin of Species... 15 Jun 2010 15:25

Experiment to prove Dirac's new-radioactivities additive-creation Chapt 5 #166; ATOM TOTALITY
Experiment: I believe the best setup is the very microscope, even though Dirac himself was pushing for a astronomical proof setup with using the Moon to Earth 2cm/year approach for additive creation. Dirac mentions work by Shapiro and Van Flandern on page 84 of his book "Directions in Physics". Trouble with an... 15 Jun 2010 15:25