What value on P gives an ellipse with 768 lattice Points? x^2 + 3y^2 = P P= 4*7*13*19*31*37*43 gives 384 lattice points
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1$\begingroup$ Using arithmetic in Eulerian integers it is straightforward to determine the number of solutions in terms of the prime decomposition of $P$. Hence this is not a research level question. Please read mathoverflow.net/help/on-topic $\endgroup$– GH from MOCommented Jan 23, 2014 at 20:44
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2$\begingroup$ Just multiply by one more prime that is $1\pmod 3$; for example $61$. $\endgroup$– LuciaCommented Jan 23, 2014 at 20:45
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For example, using $P' = P \cdot q$ where $q$ is any of $49,61,67,73,79,97$.
answered Jan 23, 2014 at 20:45
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$\begingroup$ Do they have to be? I just coded a program in Mathematica, and these values seem to work... 55? $\endgroup$ Commented Jan 24, 2014 at 19:01
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$\begingroup$ The 1/7-ellipse exsists. Can I find an 1/143-elips or an 1/429-ellipse $\endgroup$ Commented Jan 25, 2014 at 7:48
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$\begingroup$ The Shippensburg University Problemsolving Group says in Mathematics Magazine vol.60, no4p245 that 1/143 and 1/429 gives ellipses as 1/7 does. Is This true? $\endgroup$ Commented Jan 29, 2014 at 20:47