FEEDBACKS

FEEDBACKS TO MY VIDEO

After I posted my video about the first rule of divisibility by 7 of the History of Number Theory, created by me in 2005, I received a few feedbacks from experts on this matter.

I transcribe the following feedbacks I received from two reputable professionals who occupy important positions in traditional organizations of the mathematical world that together, congregate more than 800,000 math teachers around the world:

“Thank you!

Interesting indeed.

I have posted the link on the Facebook Site for …”

and

“Silvio,

This video is very interesting & I enjoyed watching it. What would be   even more interesting is a video of you explaining WHY this rule works   and HOW you developed it. Also, you used several examples, but that does not prove your rule works. Perhaps with more abstract mathematics, you could convince more people.

Sincerely,”

I do not mention their names because it seems they forgot the experts’ first commandment: “Do not appreciate the work of an outsider even if you cannot prove he is incorrect.”

My video explaining why my rule works will be posted soon.

There are also a few shy feedbacks like “Mathematically interesting” or the like.

It seems that the few experts that tried to deny my claim (“the first rule”) do not know that Mathematics is based on definitions. The rules they defend do not fit into the definition of “divisibility rule”:  “A divisibility rule is a SHORTHAND WAY of determining whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits” (Wikipedia).

The expert who apparently is the best in mental calculation alleged that it takes time to figure out "what digit should I put here to make a multiple of 7”. Anyone who knows the 7 times table is able to do this very quickly; like the Brazilian student of the primary school who tested my rule in 2006.

 Another expert cited these addresses to exemplify the existing rules of divisibility by 7 before 2005:

 (www.aaamath.com/div66_x7.htm,

www.maa.org/mathland/mathtrek_05_23_05.html,

www.math.hmc.edu/funfacts/ffiles/10005.5.shtml

Anyone can access the addresses mentioned above: THEY DO NOT PRESENT A SINGLE REAL RULE OF DIVISIBILITY BY 7!!!! The respective procedures do not fit into the definition of “divisibility rule”.

Of course, when I stated my claim I had already accessed the mentioned sites (as many others) and concluded that, according to the definition of “divisibility ruIe”, no real rule of divisibility by 7 had been created before 2005. The procedures presented in those sites, especially when applied to larger numbers, are very slow and do not fit into the definition of “divisibility rule”.

Professional mathematicians know that mathematical rules used to verify if a number is divisible by other are not rules of divisibility if they do not fit the respective definition.

There is a paper written by Prof. Bruce Ikenaga entitled “Divisibility Tests and Factoring” in which the author referred to the expert’s favorite rule this way:

“It is difficult to factor a large, arbitrary integer in a reasonable amount of time. You can use simple divisibility tests like those above to deal with "obvious" cases, but the general problem is the object of current research.”

I agree with Prof. Ikenaga.

My rules can be used quickly and precisely to test the divisibility by 7 of numbers of any magnitude.

In my next post I will comment the existing false rules for divisibility by 7 before 2005; I will explain why they work and demonstrate why their application is very slow and so they are not SHORTHAND WAYS according to the definition of divisibility rule.