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Timeline for Division problem

Current License: CC BY-SA 4.0

10 events
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Dec 11, 2022 at 11:46 history became hot network question
Dec 11, 2022 at 5:07 vote accept Benjamin L. Warren
Dec 11, 2022 at 4:21 answer added GH from MO timeline score: 11
Dec 11, 2022 at 4:19 history edited Benjamin L. Warren CC BY-SA 4.0
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Dec 11, 2022 at 3:09 comment added JoshuaZ Not a proof but a heuristic that the answer is yes: Pick an a such that $6a+1$ is prime. Then there should be a roughly 50% chance that there is a $b$ that works based on considerations about half of all residues mod $6a+1$ being quadratic residues. Possibly quadratic reciprocity can be used to come up with an explicit modulus condition for $a$ which is guaranteed to work.
Dec 11, 2022 at 2:58 comment added Benjamin L. Warren I know of no techniques in general for a question like this, and this one seems right, so I'm hoping someone can share insight as to a strategy instead of a simple yes or no.
Dec 11, 2022 at 2:57 history edited Benjamin L. Warren CC BY-SA 4.0
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Dec 11, 2022 at 2:30 comment added Conrad What is the motivation?
Dec 11, 2022 at 2:13 history edited Benjamin L. Warren CC BY-SA 4.0
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Dec 11, 2022 at 2:06 history asked Benjamin L. Warren CC BY-SA 4.0