Mistakes in Congruency Theory

Illustration of counting with calculator
Source of picture: wallpaperaccess.com

                                    Firstly, I look at this chapter of this book, after learned the middle part, they serve a made-sense facts in mathematics. Of course, people will think this chapter is 100% right. The contents are paradoxical with the part I've learned before. In fact, this is only a story of the old inventor which doesn't have any connections with this chapter.

                                    This theory we discuss here, so-called "Congruency Theory". In example 4.7, there is a small mistake but can be a big "FAULT" for math. For your information, this lesson (entitled the same with the book, "Number Theory") is taught in higher education. That was proven by reader of this book, written there as lecturer Number Theory lesson. Maybe it is still told in this area of study till now. Direct to the thing we mean, based on contradictory and half wrong definition, I found some mistakes here. In first row of arithmetic modulo equation, it supposed to be zero at forward of congruence sign. I try the last equation in my calculator, the result is not satisfactory. It must be changed with 107 in place of division remainder.

                                   Suddenly, I look at the statement in 2 base at the top of the solution. Emerge the root of cause. There are zero in this operation. I mean 0 x 2⁴. These numbers show that the-two-to-the-power-four number is going to be gone from this mathematical statement. Where the 5¹¹⁰ will not reflect the number itself. While another mistake I see on page 59. The twos must be without any power. And, they must not be added each other. But I have a solvation for this theory, although only a little. Let us figure it out in next paragraph.

                                     Complete solvation of this problem maybe found by me or other scientists. I now am going to post my formula(s) that is (are) able to find units of division yield. The formula of powered number except 1, 0, and 5 (5 has units of powered number all 5) is:

                                       Note that this formula is just valid for unit power (1 until 9). For power of 10, we use this formula (multiplying factor of 10):

                                      Whilst, if there are multiplying factor of 10 and non multiplying factor of 10, we just have to multiply the unit of it to unit of n^b (multiplying factor of 10).

                                       

                                    That's all we can discuss. If you have any questions or opinion, please comment below. I hope this content is always having benefits for all of us. Thank you for visiting my blog!

 

Bibliography:

Jupri, A. 2020. Teori Bilangan. Second published. Bandung: Yrama Widya Publishing.

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