Timeline for Finding all integer solutions of the following inequality $\bigg| \sqrt[3]{2}-\frac{p}{q} \bigg | <\frac{1}{q^{5/2}}$
Current License: CC BY-SA 3.0
4 events
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| Mar 26, 2020 at 21:56 | comment | added | Steffen Jaeschke |
A graphical solution is possible with Show[Graphics[{LightGray, Table[Point[{i, j}], {i, 0, 6}, {j, 0, 6}]}, Axes -> True], RegionPlot[Abs[Surd[2, 3] q - p] < 1/q^(3/2), {p, 0, 6}, {q, 0, 6}, Frame -> True], Graphics[{Red, Point[{1, 1}], Point[{2, 1}], Point[{5, 4}]}, Axes -> True]] to make yourself shure this are all solutions of integer pairs.
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| Sep 30, 2017 at 12:46 | comment | added | aardvark2012 |
If you don't mind specifying a range of integers to search (which, understandably, you probably do) you could use a region: reg = ImplicitRegion[Abs[Surd[2, 3] - p/q] < 1/q^(5/2), {{p, 1, 5}, {q, 1, 5}}]; and then Reduce[Element[{p, q}, reg], {p, q}, Integers] gives you the desired output.
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| Sep 30, 2017 at 11:38 | answer | added | Mariusz Iwaniuk | timeline score: 4 | |
| Sep 30, 2017 at 8:20 | history | asked | vito | CC BY-SA 3.0 |