Recent content by TTob

I need to prove that the equation x^4 - y^4 = 2 z^2 has no positive integer solutions. I have tried to present this equation in some known from (like x^2+y^2=z^2 with known solutions, or x^4 \pm y^4=z^2 that has no integer solutions) without success. Any hints ?

Thank you !

I need to prove that p congruent modulo 8 to \pm 1.

I need to prove that p congruent modulo 8 to \pm 1 for every prime divisor p of 4n^2+4n-1. 4n^2+4n-1 is odd so we have p \equiv \pm 1,3,5 \pmod{8} I don't know how to continue from here... I need some hint. Thanks.

Homework Statement Check if the following series is convergent. \sum^{\infty}_{i=1}l n(cos(\frac{1}{n})) I have tried a lot of different tests without success. I need some hint. Thanks Homework Equations The Attempt at a Solution

order isomorphism f:R-->R let f is order isomorphism from (R,<) to (R,<). why f is continuous ? so f is bijection and a<b <--> f(a)<f(b), so what ?

what is the cardinality of a set A of real periodic functions ? f(x)=x is periodic so R is subset of A but not equal because sin(x) is in A but not in R. hence aleph_1<|A|.

because this is cycle decomposition and hence c_1 is r_1-cycle,..., c_k is r_k cycle.

Homework Statement prove that there are not permutations of order 18 in S_9. Homework Equations The Attempt at a Solution let t=c_1,...,c_k is cycle decomposition of such permutation. let r_1,...,r_k the orders of c_1,...,c_k. then lcm(r_1,...,r_k) = 18 and r_1+...+r_k = 9...

Homework Statement let a=(b_1,...,b_n) n-cycle in the permutation group S_n . prove that the cycle decomposition of a^k consist of gcd(n,k) cycles of n/gcd(n,k) size. The Attempt at a Solution I know that a^k(b_i)=b_{i+k (mod n)} how can it help me ?

Thank you !

this limit equals 1 when x_i=x_k and 0 when x_i<x_k. so lim (x_1^p+...+x_n^p)/x_k^p = number of x_i that equal to x_k. I don't know how to continue.

question: let x_1,...,x_n positive real numbers. prove that \lim_{p\to \infty}\left(\frac{x_1^p+...+x_n^p}{n}\right)^{1/p}=max\{x_1,...,x_n\} can you give me some hints ?

for n=2 we have det(A) = -5. so what ?

I don't understand this : let A is n x n matrix whose entries are precisely the numbers 1, 2, . . . , n^2. Put odd numbers into the diagonal of A, only even numbers above the diagonal and arrange the entries under the diagonal arbitrarily. Then det(A) is odd. What is the explanation ?