Prime Definition and 756 Threads

Hello, I can't get this small contest problem. How do you solve this kind of problem? Let p and q be prime numbers such that (p^2+q^2)/(p+q) is an integer. Prove p=q.

Hi, I have the following (new, I think) conjecture about the Mersenne prime numbers, where: M_q = 2^q - 1 with q prime. I've checked it up to q = 110503 (M29). Conjecture (Reix): \large \ order(3,M_q) = \frac {M_q - 1}{3^O} where: \ \large O = 0,1,2 . With I = greatest i such that...

Let x1 + x2 =1 be a unit circle upon a finite field Zp where p is prime. Is there any algorithm which can give all the possible solutions (x1,x2) an element of Zp*Zp as well as the total number of such solutions? If exists, what is the complexity of it?

Homework Statement Find the gcd of 22,471 and 3,266 and express in the form 22,471x + 3,266y Homework Equations The Attempt at a Solution I know how to get the gcd of easy numbers... using the prime factorization. But how do I do that with numbers of this scale?

Ten distinct prime numbers, each less than 3000, when arranged in increasing order of magnitude describe an arithmetic sequence. What are these ten prime numbers?

Bert has some cows, horses and dogs, a different prime number of each. If the number of cows (c) is multiplied by the total of cows and horses (c+h), the product is 120 more than the number of dogs (d), that is: c*(c+h) = 120 + d. How many cows, horses and dogs does Bert have?

Homework Statement One algorithm for finding the prime factorization of a number n is the following: Starting with d = 2, and continuing until n\geqd, try to divide n by d. If n/d, then record d as a (prime) factor and replace n by n/d; otherwise replace d by d + 1. a) When d is recorded...

I stumbled across this question:Suppose that a and b are relatively prime.Prove that ab and a+b are relatively prime.

The Fibonacci numbers seem intimately connected with geometry. Prime numbers appear to avoid geometrics, however. Can you give some counterexamples of this latter statement?

The Problem A projectile is thrown from a sloping hill with an initial speed of 20m/s directed perpendicular from the slope. If the incline of the slope is 32 degrees, how far from where it is thrown will the ball land? I found these equations will result in a solution... Want: R = square...

The series of prime numbers pn=2, 3, 5, 7, 11, 13, 17, 19, 23, 27..., and Fibonacci numbers Fn=0, 1, 1, 2, 3, 5, 8, 13, 21, 34..., suggest that Fn might be considered to surpass pn exactly at an irrational value ns such that 9<ns<10 and can be determined most exactly from both series as...

What three digit prime number has all prime digits and forms primes with its first two and last two digits?

Homework Statement Let H and K be subgroups of G of finite index such that [G:H] and [G:K] are relatively prime. Prove that G = HK. The attempt at a solution All I know is that [G:H intersect K] = [G:H] [G:K]. What would be nice is if [G:HK] = [G:H] [G:K] / [G:H intersect K], for then I...

What is yhe usage of big primes in Cryptography?

We have that $P(x) = \sum_{k=1}^{\infty} \frac 1k \pi(x^{1/k})$ and $Li(x) = \int_2^n \frac {dt}{\log t}$ And the prime number theorem is: $$\pi(n) \sim \frac{n}{\log n }$$ I want to show that $$P(x) \sim Li(x)$$ is equivalent to prime number theorem. Can some body please...

Show that if H is a normal subgroup of G of prime index p, then for all subgroups K of G, either (i) K is a subgroup of H, or (ii) G = HK and |K : K intersect H| = p.

Homework Statement Let G be a group and let g be an element G such that |g| = mn, where gcd(m, n) = 1. Show that there are unique elements a, b in G such that g = ab = ba and |a| = m and |b| = n. The attempt at a solution Since gcd(m, n) = 1, there are integers s and t such that ms + nt =...

Ok, here's a challenge for you guys. Lets figure out a pattern for prime numbers.

http://www.msnbc.msn.com/id/26914730/from/ET/ Go Bruins!

Homework Statement Show the equation x^3 + 2y^3 =5 has no solution for x,y in Z, by considering it modulo a prime Homework Equations The Attempt at a Solution I need help starting this problem, I've been stuck on it for a while and don't even have a clue of how to start it. Thanks

I just turned in this homework and I want to know if I got it right. The proof is pretty simple, but I think I might be using a theorem in the wrong way. Homework Statement \{P_{i} : i \in \Lambda \} is a family of prime ideals in a ring, R. Prove that R \setminus \{ \cup_{i \in...

Problem 1 Homework Statement Prove that p^2 - 1, where p is a prime greater than 3, is evenly divisible by 24.Homework Equations The Attempt at a Solution p^2 - 1 can be written as (p+1)(p-1) Since p is a prime, (p+1) and (p-1) must both be even numbers. Since every third integer is divisible...

i need to calculate the sum of the prime numbers below 2 million i am completely stumped help! thanks

I want to find prime and jacobson radical radicals in Z[T]/(T^3), here Z = integers. Is it true that Z[T]/(T^3) is a field, because T^3 is irreducibel over Z[T]. If it is true that Z[T]/(T^3) is a field then 0 is the prime and jacobson radical radical. Is it true please help.

http://arxiv.org/abs/math/0412062"

Phi exists at the center of prime quadruplets, along with its square root, and cube root! http://www.code144.com/zphithrice.png The 'pos' numbers come from the position of the prime numbers in the sequence itself, i.e. 193 is the 44th prime number, and 197 is the 45th prime number...

I have run into a use of the symbol usually called prime (y' for example) in the description of an event. P(A or B') Please, what does it mean?

I was playing around trying to find a function which matches the prime numbers (futile, I know) when I stumbled upon this little thing: f(n) = n^2 - (n-1)^2 (for n>1, it seems) which gives f(2) = 3 f(3) = 5 f(4) = 7 f(5) = 9 (off by -2) f(6) = 11 f(7) = 13 f(8) = 15 (-2) f(9) = 17 f(10) = 19...

Homework Statement Recall that two polynomials f(x) and g(x) from F[x] are said to be relatively prime if there is no polynomial of positive degree in F[x] that divides both f(x) and g(x). Show that if f(x) and g(x) are relatively prime in F[x], they are relatively prime in K[x], where K is an...

Homework Statement Find all primes p such that \exists a,b \in \mathbf{Z} such that a^4-b^4=p. Homework Equations The Attempt at a Solution For simplicity, we can limit a and b to the positive integers. Factoring, we have p=(a^2+b^2)(a-b)(a+b). By the unique factorization...

It occurred to me that the rationals Q have also a unique prime factorization, as long as you allow negative exponents on the factorization. If a/b is a rational, then both a and b have a unique (integer) prime factorization, and the fraction can be expressed uniquely as a product of primes...

Can anyone tell me, what is so important about prime numbers in science?

reciprocals of primes summed to 1 As the other thread about sum of primes started it reminded me about the idea I had long ago. My starting point was Erathostenes sieve. It occurred to me that multiples of 2 make half of all natural numbers, multiples of 3 make 1/3 of all natural numbers and...

Homework Statement Let A = [3 2 1; 0 1 4; 4 2 1] (i) Find the cofactors C11, C12, C13, C21, C22, C23, C31, C32, C33 of A. (ii) Given that det(A) = 7, use the adjoint method to find A-1. (iii) Use the answer to part (ii) to find A-1 over the prime field Z5. The Attempt at a Solution...

A general question. A unit element is one that has it's multiplicative inverse in the ring. An element p is prime if whenever p=ab then either a or b is a unit element. Can a prime be a unit element? The answer is, i think, no but thus far I've been unable to find a contradiction.

I hope I am correct in saying that Bertrand's postulate can be rephrased this way: the maximum prime gap following prime p is p-3, if p > 3. Is this the closest proven result for the maximal prime gap? Wolfram MathWorld mentions 803 as a large known prime gap following 90874329411493, and...

if 2^n-1 is prime prove that n is prime

Hey Everyone, People keep on telling me that the biggest prime number known to man, is used for things like credit cards, how, I do not know, but I am hearing it more and more and need to know, because people think they are clever when they say it, but they have no further knowledge about...

1) Suppose that a and b are relatively prime natural numbers such that ab is a perfect square (i.e. is the square of a natural number). Show that a and b are each perfect squares. a=(a1^p1)(a2^p2)(a3^p3)...(a_n^p_n), a_i distinct primes b=(b1^q1)(b2^q2)(b3^q3)... (b_m^q_m), b_j distinct...

Homework Statement Let the prime numbers, in order of magnitude, be p1, p2 ... Prove that pn+1 ≤ p1p2...pn + 1Homework Equations The Attempt at a Solution I have no idea how to start. I think it involves reductio ad absurdum.

I've was reading about it [http://mathworld.wolfram.com/PrimeSpiral.htm] and found it intriguing, has there been a great deal of study devoted to it or is it thought of as some kind of quark? [P.S. I don't really know much about number theory, just curious]

I am confused by eta meson and eta prime meson . I can not the difference between them .anybody can help me ? who can tell me what are they made up ? some textbook say that the neutral eta meson is considered to be a quark combination (uubar+ddbar-2*ssbar)/6^(1/2),but I am still not clear.

I am confused by eta meson and eta prime meson ?what is the difference between the two ones ? who can tell me what are they made up ? please help me ! thank you very much !

i was looking for a counter example. and, I've not been able to think of any.

Hi all, Do you people know about any research concerning the number that lies around twin prime numbers? I mean: How much numbers are semi-primes, for instance. I made myself clear? Sorry for the bad grammar.

Homework Statement Let G be a finitely generated abelian group and let T_p be the subgroup of all elements having order some power of a prime p. Suppose T_p \simeq \mathbb{Z}_{p^{r_1}} \times \mathbb{Z}_{p^{r_2}} \times \cdots \times \mathbb{Z}_{p^{r_m }} \simeq \mathbb{Z}_{p^{s_1}}...

[SOLVED] Is 0 a prime? Am I missing something or is 0 a prime element in an integral domain? In the definition of prime element p of an integral domain, we only ask that the ideal generated by p, be prime. Well (0) is obviously prime because if ab=0 in an integral domain, then it is that...

So the problem is: "4:(a) Determine the prime ideals of the polynomial ring C[x, y] in two variables." "We recognize that an ideal P is prime if and only if for two ideals A and B, AB $\in$ P implies that either A or B is contained in P. So we must find " So anyways, I'm thinking that it...

Homework Statement Note: gcd(a,b) = the greatest common divisor of integers a and b (not both 0) suppose that (a,b)=1 and (a,c)=1 that is, a and b are relatively prime, and a and c are relatively prime Is the following statement true? if so prove it (bc,a)=1 I computed a few examples, and i...

Prove that if n is a perfect square, then (2^n) -1 is not prime. All I can get is that 2^n is some even number. I can't work in the perfect square part.