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-   -   Prime Numbers Book (https://www.mersenneforum.org/showthread.php?t=26067)

 paulunderwood 2020-10-10 13:40

Prime Numbers Book

13 Attachment(s)
Enjoy and criticize. It ain't no C&P but might help some. :book:

2 More downloads and I have uploaded a new version without the Euler Phi Function nonsense -- Thanks Robert.

24 more downloads and a new version is up with accumulated corrections and suggested text.

13 more downloads. The replacement (12th Oct) version corrects some grammatical errors, includes suggestions by Nick and a Lucas Sequence algorithm.

12 more downloads. The replacement (Oct 15th) makes the suggestions by Nick and corrects some typos.

4 more downloads. The replacement builds on suggestions by Nick. There is now a section on Gaussian primes. Replacement (18 Oct,2020) uploaded.

 Dr Sardonicus 2020-10-10 14:10

There is a caveat in using the term "number" to mean "natural number" or "positive integer."

Euclid distinguished between 1 ("the unit") and integers greater than 1, which he called "numbers." Thus, a "prime number" was, [i]by definition[/i] an integer greater than 1.

The unit, 1, is neither prime nor composite.

 kriesel 2020-10-10 14:28

spell check; grammar

Legendre, J[B]o[/B]cobi and Kronecker (should be Jacobi) (page 3)

[SIZE=2]"The determinant of a A is" (bottom of page 9)[/SIZE]
The determinant of a [B]matrix[/B] A is

nothing else conspicuous through page 10 on a first pass.

Pretty clean.

 Viliam Furik 2020-10-10 14:52

Page 3 - Typo in "Jocobi"
Page 32 - Fig. 7.1 contains n = 2 twice, lots of unknown where it shouldn't be (n= 61,89,107)

 R. Gerbicz 2020-10-10 15:59

On page 39:
"The Euler Phi Function is useful since for all a
a^(1+φ(n)) ≡ a (mod n)."

This is very false, a small counter-example is a=2, n=4.

 bhelmes 2020-10-10 20:46

"It is important to analize the the exponentiating" page 49.

Greetings
Bernhard

 Knut 2020-10-10 20:53

You write i were the square root of -1.

As far as I know, the square root r of a number x is the non-negative solution of the equation r^2 = x as far as real numbers are concerned.

As i is neither positive nor negative and i^2 = -1 and (-i)^2 = -1 in my opinion it is not correct to say i would be the square root of -1.

Best regards

Knut

 paulunderwood 2020-10-10 22:40

[QUOTE=Knut;559490]You write i were the square root of -1.

As far as I know, the square root r of a number x is the non-negative solution of the equation r^2 = x as far as real numbers are concerned.

As i is neither positive nor negative and i^2 = -1 and (-i)^2 = -1 in my opinion it is not correct to say i would be the square root of -1.

Best regards

Knut[/QUOTE]

I have read [url]https://en.wikipedia.org/wiki/Imaginary_unit[/url] What would you say I should write? [I]i[/I] is fixed to be one of the two square roots of [I]-1[/I]?

 paulunderwood 2020-10-10 22:43

I have tidied up what I want write about "The Fermatian Child".

I will refrain from reposting the paper until more input from folks.

 Knut 2020-10-11 05:28

I think there is no square root of -1.

Instead, define the "imaginary unit" i with i^2 = -1. And then define complex numbers.

This, in my opinion, could help to avoid disturbances.

E.g.

x^2 = 3*i
x^2 = - 3*i
x^2 = 2 + 3*i
x^2 = 2 - 3*i
x^2 = - 2 + 3*i
x^2 = - 2 - 3*i

There are two (complex) solutions of each equation, of course. Which of the two solutions is to be named the "square root"? I am not aware of a definition.

I apologize fpr my poor command of the English language and hope you can see my point.

Best regards

Knut

 Nick 2020-10-11 07:44

There are a number of errors at the start, some just details of definitions but others hiding more important points.
How it would be best to resolve these depends strongly on who you are writing this for.
What is the intended audience?

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