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So in this case, 11/2 = 5.5 and there are 5 QR's. Here I noted that if my modulo was prime then the number of quadratic residues is always less than half the prime. For example, in the case above, I would write out the quadratic residues of 11: I was using Quadratic Residues to determine whether or not my equations had solutions. I was just solving some congruence problems with prime modulo. AstroGrav is a full-featured, high precision solar system simulator that calculates the gravitational interactions between all astronomical bodies. The application offers a modern and unique EQ control system, using a variety of amazing sound effects to improve the audio output quality. AstroGrav 4.5.1 download by AstroGrav Astronomy Software.

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AstroGrav is ideal for astronomers, researchers, teachers, educationalists, and students, and comes complete with a tutorial and full documentation. Any situation in which gravity is the only significant force can be simulated, and the illustrative sample files that are included with AstroGrav include many examples such as exoplanet systems, protoplanets that evolve into planetary systems, rubble piles and their interactions with massive bodies, complex star systems, and even projectiles and bouncing balls. Because it calculates the motions of bodies from their gravitational interactions, AstroGrav is not restricted to just the solar system.

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