Let k be a positive integer.
define G_k = {x| 1<= x <= k with gcd(x,k)=1}
prove that:
a)G_k is a group under multiplication modulos k (i can do that).
b)G_nm = G_n x G_m be defining an isomorphism.
i got this problem which is killin me :tongue:
given a set {1,2,...,2n} choose any (n+1) element subset, show there exists an element which divides another element.
given a field F and two algebraic closures of F, are those two the isomorphic?
and why doesnt this show that C and A (algebraic numbers) arent isomorphic?
so embarrased askin so much :redface:
On a table there are 14 cards. On each card there is a number between 1 to 1000. Show it is possible to divide the cards into two piles so that the total sums are the same.
let alpha be algebraic over F of degree n, show that there exists at most n isomorphisms mapping F(alpha) onto a subfield of bar F (this means the algebraic closure).
thanx
im so embarrased askin so much :blushing:
show that given 5 distinct lattice points in the plane (points with integer coordinates) there exists a line segment between both of them containing another lattice point on its interior.
i just cant figure this out.
given a n x n matrix (with n>1) "A" such that all entries are integers and A is invertible such that A^{-1} also has integer entries. Let B be another matrix with integer coefficients so that:
A+B, A+2B, A+3B, ... A+(n^2)B
Are all invertible with integer...