PSfrag replacements

\frac{1776}{35}

70 \frac{3026}{35}

1776

y^{2} = x^{3} − 1776^{2}x has the nontrivial solution x = −576, y = 40320.

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?? ?? ??

2001?

y^{2} = x^{3} − n^{2}x
n = 5 :  y^{2} = x^{3} − 25x,  solution: x = −4, y = 6
n = 6 :  y^{2} = x^{3} − 36x,  solution: x = −3, y = 9
n = 1 :  y^{2} = x^{3} − x,  no nontrivial solutions (Fermat)

#{(a, b, c) : 2a^{2} + b^{2} + 8c^{2} = n}
= 2 · #{(a, b, c) : 2a^{2} + b^{2} + 32c^{2} = n}

PSfrag replacements

\frac{450660}{777923} \frac{777923}{6090} \frac{605170417321}{4737551070}

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