Prime Definition and 777 Threads

Why is it not possible for a filed to have have two prime fileds one isomorphic to Zp and the other isomorphic to Zq for p and q primes. Thank you

One of my professors told us about a prime number equation he came up with back in his own college days in Russia. It was published in a Russian journal in the problems section years and years ago and has not been translated to English. The thing is, his professor thought this equation must have...

Homework Statement prime mover = 220 hp crane = 2000 tonne velocity crane = 10m/min = 0.17m/sec acceleration crane = 0.017m/sec every 100 tonne = 6 tonne of friction 1hp = 726 W 1 tonne = 1000 kg Homework Equations how many prime mover are needed to pull the crane?prime...

I recently got interested in number theory and have been fiddling around with Scilab trying to find interesting things. I came across the following mildly interesting property, which I couldn't find much about on Google. Form the difference d_n between the sum of the squares of the prime...

I know that any prime p = 1 mod 4 can be expressed as sum of 2 squares. But how many different pairs of integers a,b such that p = a^2+b^2? (with a>b!) It seems there is only one pair. How to prove it? I try in this way: assume p = a^2+b^2 = c^2+d^2 (with a>c>d>b) and try to show it has...

Homework Statement Why are prime ideals so important? Homework Equations The Attempt at a Solution

Homework Statement Let D = Z[sqrt(10)], and let P be the ideal (2,sqrt(10)) 10). Prove that P is a prime ideal of D. Homework Equations The Attempt at a Solution Not sure where to start. I think elements are of the for a+b*sqrt(10), a,b integers. Any hints as to what to do next?

Is there any method to show that their are infinitley many prime numbers?

how do you prove, if p is prime, then a derived equation of p is prime, if true?

I need to do all the Physics-Book purchasing I can very soon! I have Mary Boa's book, Div Curl Grad and all that, and some others on the list. What else would be great to have? I'm starting calc III and DEQ next semester (I have the textbooks already), and I am interested in Optics...

I want somebody to help me what attempts have been made to understand the sequence of prime number. Is the Nth term of the sequence disclosed?

Homework Statement If p and q are prime numbers, p>q>2 , and 1+k*p divides q^n for some positive integer n. What can i expect of the values of k ? Does it works just for k=0 ? Homework Equations q^n = 1 (mod p) The Attempt at a Solution I know that k=0 works , and k=odd don't...

Homework Statement Find all zero divisors of the ring Z17 Homework Equations Are there any zero divisors of the ring Z17? The Attempt at a Solution I multiplied 17*17=289...that is only divisible by 17, so I do not think there are any zero divisors...am I missing something?

Is there a name for prime numbers whose digits sum to a prime number? For example, the prime 83 gives 8+3=11, a prime. Is there anything known about these primes, e.g. are there infinitely many of them? Thanks, M

I am trying to understand how I can find the square root of a large prime number in the form of an integer value, the portion after the decimal is irelevant. The numbers I wish to compute range around 188 multiplied by 3 to the power of 6548 plus 1, as an example. so let's say in excess of...

Let R be a ring with ideals I, J, and P. Prove that if P is a prime ideal and I intersect J is a subset of P, then I is a subset of P or J is a subset of P.

This sieve is similar to the Sieve of Eratosthenes but is very different in its implementation. Instead of considering all the numbers below N to find the primes, this sieve considers only N/3 since we know that 2/3 of the numbers up to N are multiples of 2 and 3. No numerical experiment has...

A while back I posted a question about this series on the General Math forum and was brought to task for not showing any math. My hope is to prove that these series are infinite. http://oeis.org/A002378" are the series 0,2,6,12,20,30... and distances between consecutive numbers are increasing...

scratch that. is 5606701775893 a prime number?

CONJECTURE: Subtract the Absolute Values of the Stirling Triangle (of the first kind) from those of the Eulerian Triangle. When row number is equal to one less than a prime number, then all entries in that row are divisible by that prime number. Take for instance, row 6 (see below). The...

Here is a visual prime pattern: http://plus.maths.org/content/catching-primes I have developed one of my own based upon trig, square roots and the harmonic sequence. Here is an animation/application that shows the formula visually: http://tubeglow.com/test/Fourier.html Thoughts? Questions?

What was the unsolved prime number equation? Ok so at math today my teacher told us just for fun about a math equation(wasnt really paying attention) this equation is an equation that tells where on a linaer graph prime numbers are zero, it was able to predict a prime number or something on a...

I'm confused about how difficult is it to factor numbers. I am reading that it is used in encryption and it is computationally difficult, but it seems to take O(n) from how I see it. For example to factor 6, I would (1) divide by 2 and check if the remainder is 0 (2) divide by 3 and check...

I know that the fundamental theorem of arithmetic states that any integer greater than 1 can be written as an unique prime factorization. I was wondering if there is any concept of negative prime numbers, because any integer greater than 1 or less than -1 should be able to be written as n = p1...

Homework Statement Let R = Z[x] be a polynomial ring where Z is the integers. Let I = (x) be a principal ideal of R generated by x. Prove I is a prime ideal of R but not a maximal ideal of R.Homework Equations The Attempt at a Solution I want to show that R/I is an integral domain which...

Homework Statement Prove that the product of primes between m+1 and 2m is less than C(2m,m) Homework Equations The Attempt at a Solution I have that it is less than (2m)!/m! = m!C(2m,m) which is just the product of all of the numbers from m+1 to 2m. Any help is appreciated. Even...

(p-1)! = -1(mod p), where p is a prime I have tried small values of p but I can't find any pattern. Can anyone give me some hints or directions? I don't know a detail proof. Thank you

If the universe started with a big bang, what caused that ? If you subscribe to multi-verse theory, I can ask the same question "what caused them?" and so on. If the universe always was, then anything that could've happened already happened. I already typed this statement and know the answer to...

Homework Statement Let K be a field, and f,g are relatively prime in K[x]. Show that f-yg is irreducible in K(y)[x]. Homework Equations There exist polynomials a,b\in K[x] such that af+bg=u where u\in K. We also have the Euclidean algorithm for polynomials. The Attempt at a...

Homework Statement My domain i numbers of form 4k+1. n divides m is this domain if n=mk for some k in the domain. A number is prime in this domain if its only divisors are 1 and itself. My problem is to find a number in the domain with multiple prime factorizations. Homework Equations...

The guiding premise of this thread is the following proposition: If fractals play a role in the behavior of partitions, then maybe, just maybe, they play a role also in the positioning of the primes; and if they do, then who is to say that the two, prime numbers and partition numbers, cannot at...

is there any proofs for: "for any natural (n) there are prime numbers from n to 2n,including" ??

If a and 77 are relatively prime, show that for positive integers n, a^(10^n) modulo 77 is independent of n. I think I don't understand what this statement is asking. a^(10^n) modulo 77 independent of n means that a^(10^n) modulo 77 is always going to be the same or something?

Homework Statement Let p be a prime number, and let D = {m/n| m,n are integers such that p does not divide n} Verify that D is an integral domain and find Q(D) Homework Equations i am unsure where to use the fact that a prime number divides n in this proof. I know how to check that D is an...

Homework Statement If G is a finite simple group and H is a subgroup of prime index p Then 1. p is the largest prime divisor of \left|G\right| (the order of G) 2. p2 doesn't divide \left|G\right| I think I have this proved, but want to confirm my reasoning is sound. this problem is...

Dear all, here is the new approach how to prove the Fermats Last theorem for the prime powers of n. Thank you all that you have mentioned the Diophantine equations. The proof has still one missing link. It should be proved that l is coprime to (c-b) and the same kind of proof should arise for...

Hi, I am taking a class in Linear Algebra II as a breadth requirement. I have not studied Algebra in a formal class, unlike 95% of the rest of the class (math majors). My LA2 professor mentioned the following fact in class: "The number of elements of a finite field is always a prime power and...

Is the following statement true ? Any odd prime number is congruent to either 1 or 3 mod 4. If yes , then how we could prove it ?

OK, I need help putting this into mathematical notation. 2 and 3 being the first two prime numbers make up the basic pattern in primes of 6(n)+-1 which accounts for 2/3 of all factorable numbers giving way to highly composite numbers. This factorability is the reason a base 12 system lends...

I have read several books on the Riemann Hypothesis and have a general understanding of the non-trivial zeros and their real part 1/2. In my own studies I have devised a root system based upon some of Euclid’s ideas and congruence that identifies some interesting properties of the square roots...

In a noetherian ring, why is it true that there are only a finite number of minimal prime ideals of some ideal? (And is it proven somewhere in the Atiyah-mcdonald book?)

Homework Statement Euclid's proof Euclid offered the following proof published in his work Elements (Book IX, Proposition 20)[1] and paraphrased here. Take any finite list of prime numbers p1, p2, ..., pn. It will be shown that some additional prime numbers not in this list exist. Let P be...

Homework Statement If G is an abelian simple group then G is isomorphic to Zp for some prime p (do not assume G is a finite group).Homework Equations In class, we were told an example of a simple group is a cyclic group of prime order.The Attempt at a Solution Let G be an abelian simple...

Let x, y, n all represent positive integers in x^4+nY^4. It seem there is a lot of primes in this set. In fact, even allowing x=1, n=1, we look at 1+Y^4, we see pairs, y=1, f(y)=2, (2,17), (4,257), (6,1297), (16,65537), (20,160001) Possibly an infinite set? Take the case of x=1, n=2, giving...

for... p'_n = {1 Union Prime Numbers} M_n = n-th Mersenne Number (2^n - 1) T_n = n-th Triangular Number (n^2 + n)/2 x = {0,1,2,3,13} --> F_(0, 1/2, 3, 4, 7) for F_n = n-th Fibonacci Number Then... ((p'_x*p'_2x)*(M_x - (T_x - 1))) / ((T_(M_x) - T_(T_x - 1)) is in N EXPANSION ((1*1)*(0 +...

Find all prime numbers p that can be written p = x4 + 4y4 , where x, y are positive integers.

Does anyone have any comment on the usefulness of the following test? Input P Prime = true Triangular = 0 n = 0 Do until Triangular > P n = n + 1 Triangular = Triangular + n loop X = Triangular Mod P Do Y = Int(Sqr(2*X)) ' Comment if X is triangular then (Y*Y+Y)/2 = X If (Y*Y+Y)/2 =...

Question: Suppose p and q are distinct primes. Show that p^(q-1) + q^(p-1) is congruent to 1 modulo pq. Answer: I know from Little Fermat Theorem that p^(q-1) is congruent to 1 modulo q and q^(p-1) is congruent to 1 modulo p, but I have no idea how to combine these two.

Homework Statement Largest known prime is the no... P = 2216091-1 consisting of 65050 digits. Show that there exists another prime that ends in the same 65050 digits as P.Homework Equations none The Attempt at a Solution Sorry, but I have totally no ideas for this one. Comes from a Math...

I was writing a program to find if a given number is prime or not. I can't figure out what the error is. /* To check if a number is prime*/ #include <iostream> #include <cmath> using namespace std; int main() { float a; int p,i,f=0; p=sqrt(a); if(a %...