I hope you can see WHY they work. The WHY is not far from a proof. I am sure that tons of other people know this and these divisibility tests are "well known facts." That is written in a text book somewhere. A "Well Known Mathematical Fact" is like a famous mathematician. Oxymoronic isn't it. - ThreadSky

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elviszap.bsky.social • 80 days ago

I hope you can see WHY they work. The WHY is not far from a proof. I am sure that tons of other people know this and these divisibility tests are "well known facts." That is written in a text book somewhere. A "Well Known Mathematical Fact" is like a famous mathematician. Oxymoronic isn't it.

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elviszap.bsky.social•79 days ago

To test for div by 67, first multiply 67 by 3. The result is 201. So multiply the last digit by 20 and subtract the result from the priors. Look at 4891. 1x20=20, 489-20=469. 9x20=180. -180+46=134. 4x20=80.80-13=67.

elviszap.bsky.social•78 days ago

So yesterday, after I wrote about 63, I had a computational misstep. To test for div by 73: Multiply the 1s place by 22 and add to the priors. Look at 219=3x73. 9x22=198. & 198+21=219. It's stable under this op. For 4891. 22+489=511. & 22+51=73.

elviszap.bsky.social•78 days ago

To test div by 83: Multi the 1s place by 25, and add to the priors. Consider 7221: 25+722=747. 7x25= 175. 175+74=249. But 9x25=225. and 225+24=249=3x83. Another stable point. So 7221 is div by 83. To factor: 7221=3x2407. 240+21=261. 26+3=29. 7221=3x29x83. BTW, 29 is the 1st possible prime factor.

elviszap.bsky.social•78 days ago

Finally, 3x97=291. So to test for div by 97, multiply the 1s place by 29 and subtract it from the priors. Consider, 9021. 902-29=873. 3x29=87. So 9021 is div by 97. Of course one might see that 9021=93x97 and 7221=83x87 b/c of diff of sqs. Time 4 some of my own math now b4 return for the proofs.

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