there is solution to the abc conjecture

[Giovanni Di Savino]

1. Michele, my nephew, is keen to point out that he is not 3 but almost 4 years old and yesterday Sunday he came to visit his grandparents and, even if he is not talkative, he shows off the new things he learned in nursery school. During one of his stories, I seemed absent to him and, to get my attention, he began to spell out and repeat the word pyramid. The new word said by Michele struck me and made me think of Thales' well-known measurement of the pyramids (1). Explained below, I am proposing it as a solution to the ABC conjecture and I hope you agree with me that the credit for this discovery goes to Michele who: suggested "pyramid" to me and which, he would like to point out, does not have 3 but has almost 4 years.

1.1 Thales measures the height of the inaccessible pyramid of Cheops by comparing two shadows on the ground and, knowing the height of a rod generating a shadow, he was able to determine the height of the pyramid generating the other shadow and from that measurement it is known and demonstrated that everything that can be reported on the plan can be measured. Triplets of natural numbers which on the plane are defined with the name of abscissa (x), ordinate (y) and quota (z), can represent and measure: a) all numbers that are the sum of two numbers, zc=xa+ yb; b) all numbers that are the product of two numbers, zc=xa*yb. All the natural numbers are represented on the plane but we will never have the time, space and computing power necessary to know how many the natural numbers represented are and how they are generated; we will never be able to claim to have verified how all the natural numbers represented are generated, also because, for each number, there is always the next number which will never have been verified but which exists, how they exist and may not be known: all prime numbers ≤ zc and all the numbers "c" and "d" which with c=a+b and the numbers d=rad(abc) determine by how much and when c<>d :"the solution of the abc conjecture". Thales, in subsequent days, at the same time, with the same rod or with the same one that measured the pyramid of Cheops, could have generated the shadows again to measure all the pyramids that were as high as the one already measured and would have been able to measure , also, pyramids and artefacts of different heights as long as their heights were divisible by the same measure which, today with the Fundamental Theorem of Arithmetic. we know, it can only be a prime factor of the comparison shadow generating rod. If an rod could compare and measure two artifacts of different heights, the number "c" and the number "d", which are two integer and different numbers of the abc conjecture, can be compared and measured with a measure that is equal and present in both "c" and "d"; this measurement is one of the factors of the number c. Only in this way, even if the processing times will not allow us to know the result, it is known when, how and by how much c<>d. The numbers c and numbers d can be of any size, they are represented on the plane, they exist, they are measurable and comparable with a prime number that exists even if it is not known. That prime number present in "c" and in "d", is the factor prime number rad(c) present in "c" which is =a+b, and present in "d" which is = rad(abc). The rarely reported in the statement has a well-defined mathematical meaning.

2. Thales measures the height of the inaccessible pyramid of Cheops by comparing two shadows on the ground and, knowing the height of a rod generating a shadow, he was able to determine the height of the pyramid generating the other shadow and from that measurement it is known and demonstrated that everything that can be reported on the plan can be measured. Triplets of natural numbers which on the plane are defined with the name of abscissa (x), ordinate (y) and quota (z), can represent and measure: a) all numbers that are the sum of two numbers, zc=xa+ yb; b) all numbers that are the product of two numbers, zc=xa*yb. All the natural numbers are represented on the plane but we will never have the time, space and computing power necessary to know how many the natural numbers represented are and how they are generated; we will never be able to claim to have verified how all the natural numbers represented are generated, also because, for each number, there is always the next number which will never have been verified but which exists, how they exist and may not be known: all prime numbers ≤ zc and all the numbers "c" and "d" which with c=a+b and the numbers d=rad(abc) determine by how much and when c<>d :"the solution of the abc conjecture". Thales, in subsequent days, at the same time, with the same rod or with the same one that measured the pyramid of Cheops, could have generated the shadows again to measure all the pyramids that were as high as the one already measured and would have been able to measure , also, pyramids and artefacts of different heights as long as their heights were divisible by the same measure which, today with the Fundamental Theorem of Arithmetic. we know, it can only be a prime factor of the comparison shadow generating rod. If an rod could compare and measure two artifacts of different heights, the number "c" and the number "d", which are two integer and different numbers of the abc conjecture, can be compared and measured with a measure that is equal and present in both "c" and "d"; this measurement is one of the factors of the number c. Only in this way, even if the processing times will not allow us to know the result, it is known when, how and by how much c<>d. The numbers c and numbers d can be of any size, they are represented on the plane, they exist, they are measurable and comparable with a prime number that exists even if it is not known. That prime number present in "c" and in "d", is the factor prime number rad(c) present in "c" which is =a+b, and present in "d" which is = rad(abc). The rarely reported in the statement has a well-defined mathematical meaning.

3. With "almost" 4 years old Michele and almost 78 I, we are both out of quota for the prizes but it is nice if you tell us if we have and where we have not done a good job.

(1)http://www.gioiamathesis.it/index_file/giornale_file/articoli_file/pubblicazioni_file/La%20Scienza%20di%20Talete.pdf
(2)https://vixra.org/abs/2308.0186