Using the Langlands Program Numberphile video as an excuse to play with Wolfram-Cloud/Mathematica
In this video we take the Numberphile video on The Langlands Project (featuring Edward Frenkel) as an excuse to play with Wolfram-Cloud/Mathematica. Starting with the elliptic equation y^2 + y = x^3 -x^2 , we write some code to count the number of solution where x, y and the quantities on the left and right-hand sides of the equation are integers modulo some prime p. We collect a list of primes p and the corresponding quantity a(p) which is the prime - the number of solutions for that prime. We then jump over for a "Harmonic" (?) generating function whose coefficients of prime powers match what was found in the previous list. This exercise uses the following Mathematica methods: For, Mod, If, PrimeQ, AppendTo, Product, Series, SeriesCoefficient, ListPlot, Plot, and Show
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