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  1. K

    Prove that sin (n^2) + sin (n^3) is not a convergent

    Prove that \sin (n^2) + \sin (n^3) is not a convergent sequence.
  2. K

    Set into Group

    I have seen this problem a long time ago. It is really supprising, maybe you shall like it as well. Given any non-empty set we can define a binary operation on this set to turn it into a group.
  3. K

    Galois Solvable Group

    Galois Group Is G realizable over \mathbb{Q} given that |G|=p^n ?
  4. K

    Ideal Number

    For what values does \mathbb{Z}[\zeta] have unique factorization? I know Kummer shown that \zeta being a 23-rd root of unity fails to have unique factorization.
  5. K

    Fermat's equation.

    Consider the Diophantine equation: y^3 = x^2 + 2 Without using rational elliptic curves and unique factorization in \mathbb{Z}[\sqrt{-2}] how many different ways can you show that this equation has only a single solution. Historical question: Who was the mathematician who created the...
  6. K

    Good books for PDE's

    I am sure this has been discussed a lot here since this is a physics forum. But I want to make a list of what I think is good if you want to learn them. Elementary 1)Partial Differential Equations and Boundary Value Problems with Fourier Series. This book is as simple as it gets. So even...
  7. K

    Degree of Extension

    Let p_1,p_2,...,p_n be distinct primes. Show that [\mathbb{Q}(\sqrt{p_1},\sqrt{p_2},...,\sqrt{p_n} ) : \mathbb{Q}]= 2^n
  8. K

    Fun Divisibility Problem

    Show that for any n>1 we can construct a positive integer consisting of only 1's and 0's such that this integer is a multiple of n.