Recent content by qaz

anyone? please help!

(i) Let A=A' be an nxn symmetric matrix with distinct eigenvalues la1, la2, ..., lan. Suppose that all eigenvalues lai > 0. Prove that A is positive definite: That is, prove that z'Az > 0 whenever z ne 0. (Hint: Consider the spectral decomposition of A.) ? (ii) Let A=A' be a 2x2...

ok, i know that 205 can be written as the following: (205/n)=(5/n)(41/n), which reduces to =(-1)(-1)=1. so there are either 2 cases for this problem, (5/n)=1 or (41/n)=1.

hmmm, ok, but i still don't see how you can apply that to get further.

ok, but i am stil stuck i don't know where to go from here...we don't have a good book for this class and it wasnt explained well at all.

show that the polynomial g(x)=(x^2 -5) (x^2-41)(x^2-205) has a solution modulo any integer n∈ℕ.

i am having some trouble with this problem. show that there are infinitely many integers n so that n^2+(n+1)^2 is a perfect square. (reduce to pell's equation). i know pell's equation but don't know how to apply it with this problem. pell's equation: n*x^2 + 1 = y^2. -thanks.