How a Strange Grid Reveals Hidden Connections Between Simple Numbers

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Jim1348

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Message 3116 - Posted: 25 Sep 2021, 19:20:43 UTC

In 1983 the prolific conjecturer Paul Erdős posed a math problem: Take any set of numbers you like. These could be the whole numbers from 1 to 12, the first 10,000 prime numbers, or the dates of every birthday in your extended family. Arrange these numbers in a square grid, with your list of numbers arranged both across the bottom and up one side. Then fill in the grid with either the sums or the products of the crosswise pairs.

Erdős and his collaborator on the problem, Endre Szemerédi, were interested in the number of distinct entries in such a grid. (By “distinct,” they meant that if a number appears twice — for instance, if the number 4 appears as a product of both 1 × 4 and 2 × 2 — you only count it once.) They conjectured that the number of distinct entries in either the sum or the product grid (or both) must be at least a certain value. They even established an exact threshold that the number of distinct sums or distinct products always had to meet.
https://getpocket.com/explore/item/how-a-strange-grid-reveals-hidden-connections-between-simple-numbers?utm_source=pocket-newtab

I have no idea if this is at all relevant here, but it looks like it could lend itself to a computer project.
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Message 3117 - Posted: 26 Sep 2021, 16:02:29 UTC - in response to Message 3116.  

Interesting article. No relation to number fields as far as I can see, but yes it would make a good BOINC project.
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Message boards : Science : How a Strange Grid Reveals Hidden Connections Between Simple Numbers


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