Recent content by jaci55555

  1. J

    Prove a^n - a is multiple of n

    yay, got it all! thank you for all your help everyone! i'd put up the soln but you all had it ages ago :P
  2. J

    Connection between roots of polynomials of degree n

    :) you rock my world! are you really still in high school?
  3. J

    Prove a^n - a is multiple of n

    before i can suppose this, i need to prove it true for a^5 - a... which i haven't got yet i think it'll work for every n prime
  4. J

    Prove a^n - a is multiple of n

    my computer doesn't let me see your replies until i post something. very frustrating
  5. J

    Prove a^n - a is multiple of n

    ooh, didn't see your reply! yes, you're right, just fixed it
  6. J

    Prove a^n - a is multiple of n

    no, (a-1)^5 = a^5 - 5a^4 +10a^3 - 10a^2 + 5a -1
  7. J

    Connection between roots of polynomials of degree n

    algebrat: at n=1 it is just the reciprocal at n =2 it's: x_1 = (a_1 +- sqrt(a_1^2 -4a_2a_0))/2a_0 and x_2 = (a_1 +- sqrt(a_1^2 -4a_2a_0))/2a_2 so everything above the line is he same, just the a_0 and a_2 change i'll find a formula for n =3 and try that... dick: i tried this, but don't see...
  8. J

    Prove a^n - a is multiple of n

    thanks dickfore, but Dh is right, it's just to figure out if there is any generalization :) thanks tho! Algebrat: It's a post-grad class where they give us random problems to set to young children in an understandable way DH: (a+1)^5 = a^5 + 4a^4 + 6a^3 + 4a^2 + a^1 so we have the a^5 and...
  9. J

    Connection between roots of polynomials of degree n

    Homework Statement The two polynomial eqns have the same coefficients, if switched order: a_0 x_n+ a_1 x_n-1 + a_2 x_n-2 + … + a_n-2 x_2 + a_n-1 x + a_n = 0 …….(1) a_n x_n+ a_n-1 x_n-1 + a_n-2 x_n-2 + … + a_2 x_2 + a_1 x + a_0 = 0 …….(2) what is the connection between the roots of...
  10. J

    Prove a^n - a is multiple of n

    Homework Statement Prove that a^3 - a is a multiple of 3 a^5 - a is a multiple of 5 Generalise … to a^n - a a multiple of n Homework Equations The Attempt at a Solution a^3 - a = a(a^2 - 1) = a(a+1)(a-1) thus three consecutive numbers are multiplied. if three numbers are...
  11. J

    Proving Convergence of sum[n=0 to inf] (z+2)^(n-1)/((n+1)^3 * 4^n) for |z+2|<=4

    so i remove the lim and then |Z+2|<4, but i still need it to be equal to 4 as well
  12. J

    Find Entire Functions for f(2-i)=4i and |f(z)|≤e^2

    thank you
  13. J

    Proving Convergence of sum[n=0 to inf] (z+2)^(n-1)/((n+1)^3 * 4^n) for |z+2|<=4

    So then lim(n->inf) (z+2)/4 <1 so that lim(n->inf) (z+2) <4 but i need to find find <=4
  14. J

    Proving Convergence of sum[n=0 to inf] (z+2)^(n-1)/((n+1)^3 * 4^n) for |z+2|<=4

    Thank you for answering, I'm still figuring LaTeX out :) so should i use what i did, and then the ratio test? I did this and got lim (0-> inf) ((n+1)^3/(n+2)^3), are there any steps i should put after this, or is it fine that i can see that this is <1 ? Thanks again for you help!
  15. J

    Find Entire Functions for f(2-i)=4i and |f(z)|≤e^2

    Thanks for answering :) That is all the question stated - so i think it does hold for all z. I thought the theorem i stated above WAS Liouville's theorem? But i wasn't sure about how to use it.