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Forum: Number Theory Discussion Group 2021-06-04, 13:04
Replies: 1
Views: 408
Posted By Charles Kusniec
Divisibility between polynomial expressions

Given the expression
[$$]x = \frac{n^2 -bn}{(2n+k)-b}[/$$]
For [$]b[/$] an integer coefficient, [$]k[/$] is any integer constant, and index −∞<[$]n[/$]<∞.
What is the relationship that must exist...
Forum: Number Theory Discussion Group 2021-05-08, 16:50
Replies: 6
Views: 1,192
Posted By Charles Kusniec
Dear a1call, Thanks for the example. ...

Dear a1call,

Thanks for the example.

I like you used 65 as an example, because this is one of those cases of multiplicity of primitive Pythagorean triangle.

At 65, we have 2 solutions...
Forum: Number Theory Discussion Group 2021-05-08, 13:46
Replies: 6
Views: 1,192
Posted By Charles Kusniec
Actually, we have 2 trivialities for n. We have...

Actually, we have 2 trivialities for n. We have n=0 and n=1 as trivialities. I agree with what you said. What I am complementing is that there is another way to do this proof and in it we have to use...
Forum: Number Theory Discussion Group 2021-05-08, 10:38
Replies: 6
Views: 1,192
Posted By Charles Kusniec
Dear Dr Sardonicus, I read your proof and found...

Dear Dr Sardonicus, I read your proof and found no fault. Apparently it is perfect. Congratulations. I think the way I asked already giving the answers helped. Now, the challenge is to find at least...
Forum: Number Theory Discussion Group 2021-05-08, 00:09
Replies: 6
Views: 1,192
Posted By Charles Kusniec
A pretty good challenge

A PGC (pretty good challenge). Given:

x=(y^2-(n^2-n))/(2n-1)=(y^2-Oblong)/Odd

To prove,

1. If n>0, there will be Integer solution for x iff (2n-1) are the numbers that are divisible only by...
Forum: Miscellaneous Math 2020-08-23, 10:50
Replies: 6
Views: 2,623
Posted By Charles Kusniec
Where is the weakness of this reasoning?

Let’s be any two positive and/or negative Odd Primes P1 and P2.

Because both are Odd Primes, there will always exist an Integer reference r equidistant from them such as:

P1=r+d

P2=r-d
...
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