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  • Mathematics Stack Exchange
    Q A for people studying math at any level and professionals in related fields
  • Legendres three-square theorem - Mathematics Stack Exchange
    Legendre's three-square theorem Ask Question Asked 5 years, 4 months ago Modified 1 year, 9 months ago
  • inequality - Taking the square roots in inequalities - Mathematics . . .
    7 I have a question regarding taking square roots in inequalities I have a problem asking: Suppose $3x^2+bx+7>0$ for every real number x Show that $|b|<2\sqrt {21}$ In an earlier question it was established that I couldn't take the absolute value of both sides since it is not an equation
  • Find the Square Root - Mathematics Stack Exchange
    MULTIPLE PRIMES Again, if a square root exists, there are two square roots modulo each prime So if we are using multiple primes, there can be more square roots For example, with two primes, there are 2 square roots modulo the first prime and two square roots modulo the second prime This gives us $2 \cdot 2 = 4$ square roots
  • When does a Square Matrix have an LU Decomposition?
    When can we split a square matrix (rows = columns) into it’s LU decomposition? The LUP (LU Decomposition with pivoting) always exists; however, a true LU decomposition does not always exist
  • How do I square a logarithm? - Mathematics Stack Exchange
    $\log_2 (3) \approx 1 58496$ as you can easily verify $ (\log_2 (3))^2 \approx (1 58496)^2 \approx 2 51211$ $2 \log_2 (3) \approx 2 \cdot 1 58496 \approx 3 16992$ $2^ {\log_2 (3)} = 3$ Do any of those appear to be equal? (Whenever you are wondering whether some general algebraic relationship holds, it's a good idea to first try some simple numerical examples to see if it is even possible
  • Square Inches vs Inches Squared - Mathematics Stack Exchange
    An inch squared is a 1” x 1” square, not a linear one dimensional inch That’s why 12 inches squared is 12 square inches, whether 6x2, 3x4, or 12x1 Taken literally, 12 inches squared would simply be a linear 144” and in no way refer to area Then it would be written 12^2 inches, not 12”^2
  • Square roots in the $p$-adics - Mathematics Stack Exchange
    Suppose $ (n,p) = 1$ and $n$ is a square mod $p$, so the square root in $ {\mathbb Q}_p$ should exist One quick way to explicitly find good approximations of it is Newton's method
  • Prove that the square root of 3 is irrational [duplicate]
    The number $\sqrt {3}$ is irrational ,it cannot be expressed as a ratio of integers a and b To prove that this statement is true, let us Assume that it is rational and then prove it isn't (Contradiction) So the Assumptions states that : (1) $\sqrt {3}=\frac {a} {b}$ Where a and b are 2 integers Now since we want to disapprove our assumption in order to get our desired result, we must show
  • Square Fibonacci numbers - Mathematics Stack Exchange
    Here is a paper of Bugeaud, Mignotte, and Siksek proving that the only perfect powers in the Fibonacci sequence are 0, 1, 8, 144 Therefore the only squares are 0, 1, and 144





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