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    Solving second-order ODE with Runge-Kutta 4

    Homework Statement Note: I think there is a typo here but I'm not sure. Is there supposed to be a comma between the delta t/2 and y_n on K2 and K3, and delta t and y_n on K4? Homework Equations See above. The Attempt at a Solution Substituting dy/t = z gives \frac{dz}{dt} = 3z - 2ty -...
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    Polynomial finite fields; ElGamal decryption

    Thanks, that helps. Yes, I do know Fermat's little theorem, I feel silly now for not thinking of it.
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    Polynomial finite fields; ElGamal decryption

    Homework Statement Given some ElGamal private key, and an encrypted message, decrypt it. Homework Equations Public key (F_q, g, b) Private key a such that b=g^a Message m encrypted so that r=g^k, t=mb^k Decrypt: tr^-a = m The Attempt at a Solution My problem is finding r^-a...
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    Convergence of a series

    Compare it to \sum \frac{2^n}{3^n} \frac{2^n}{3^n}\cdot\frac{3^n-1}{2^n} \frac{3^n}{3^n} - \frac{1}{3^n} 1- \frac{1}{3^n} With limit n->infinity, this = 1
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    Legendre polynomials and binomial series

    Sorry, I wrote the original question in a slightly confusing way. Anyways, I solved it last night: http://imgur.com/anpYO http://imgur.com/lEjtc.jpg
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    Legendre polynomials and binomial series

    Homework Statement Where P_n(x) is the nth legendre polynomial, find f(n) such that \int_{0}^{1} P_n(x)dx = f(n) {1/2 \choose k} + g(n) Homework Equations Legendre generating function: (1 - 2xh - h^2)^{-1/2} = \sum_{n = 0}^{\infty} P_n(x)h^n The Attempt at a Solution I'm not sure if that...
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    Hill cipher - two plaintext pairs encrypt to same ciphertext

    Homework Statement Given the following key, find two plaintext pairs that encrypt to the same ciphertext. \begin{pmatrix} 9 & 5 \\ 7 & 3 \\ \end{pmatrix} (mod \ 26) Homework Equations The Attempt at a Solution Let the two plaintext pairs be (a, b) and (c, d). Let the...
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    Related rate

    Here's how I would do it: First, make one equation. So f(t) - g(t) Then find the derivative of that equation for both t<3 and t>3. From there you should be able to find the answer to ( a ). Derivatives describe the behavoir of the original equation. They give the slope of the tangent to the...
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    Find horizontal asymptotes of a radical function

    I fixed the brackets, and I'll try that tomorrow (I'm going to bed now). Thanks.
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    Find horizontal asymptotes of a radical function

    Homework Statement Find the horizontal asymptotes for the following equation: Homework Equations f(x) = \sqrt{x^2+4x}-\sqrt{x^2+x} The Attempt at a Solution First I factored f(x): f(x) = \sqrt{x}\sqrt{x+4}-\sqrt{x+1} Then I conjugated it: f(x) =...
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