p || (a + b + c) and p !| abc

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Simon Roberts

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Dec 8, 2022, 12:40:14 AM12/8/22
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p || (a + b + c)
p !| abc
p is an odd prime
a, b, and c are pairwise co-prime integers

Does p || (ab + bc +ca)? Ever?


Also,
u and v are coprime non zero integers
i > 2 is an integer
p is an odd prime
p !| (u +/- v)


(u^p +/- v^p ) = (u +/- v )^p (mod p^i)
Are there any solutions? Specifically when v=1?


Simon
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Simon Roberts

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Dec 8, 2022, 9:01:14 AM12/8/22
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On Thursday, December 8, 2022 at 2:05:53 AM UTC-5, bwr fml wrote:
> On Wednesday, December 7, 2022 at 9:40:14 PM UTC-8, simonro wrote:
> > p || (a + b + c)
> > p !| abc
> > p is an odd prime
> > a, b, and c are pairwise co-prime integers
> >
> > Does p || (ab + bc +ca)? Ever?
> a=b=c=1 p=3?
I can't argue with that.
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David Parker

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Dec 9, 2022, 4:14:09 PM12/9/22
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Learn the difference between an expression and an equation.


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