The ABC Conjecture
The ABC conjecture states that there will only be finitely many examples where C counts as much greater then rad(abc). Here we state that A + B = C are three co-prime integers and that rad(abc) represents the multiplication of all the distinct primes which divide any of A,B and C (see unsolved problems.org). The problem is to prove or disprove the conjecture. We begin by defining the axioms of this proof—they are:-
1/ There exists an infinite number of even integers.
2/ There exists an infinite number of odd integers.
3/ There exists an infinite number of prime numbers (Euclid’s proof).
4/ There are fewer prime numbers than there are ordinal numbers
5 The frequency of prime numbers in the number line decreases with distance from the origin 1……∞
6/ Each equation of the form A + B = C contains at least one even number because even plus even equals even. Odd plus odd equals even and odd plus even equals odd.
We are examining here five separate series of numbers which are:-
1/ 2 + 2 = 4
2/ 2 + 4 = 6
3/ 1 + 2 = 3
4/ 2 + 3 = 5
5/ 3 + 5 = 8
1/ There exists an infinite number of even integers.
2/ There exists an infinite number of odd integers.
3/ There exists an infinite number of prime numbers (Euclid’s proof).
4/ There are fewer prime numbers than there are ordinal numbers
5 The frequency of prime numbers in the number line decreases with distance from the origin 1……∞
6/ Each equation of the form A + B = C contains at least one even number because even plus even equals even. Odd plus odd equals even and odd plus even equals odd.
We are examining here five separate series of numbers which are:-
1/ 2 + 2 = 4
2/ 2 + 4 = 6
3/ 1 + 2 = 3
4/ 2 + 3 = 5
5/ 3 + 5 = 8
To read the whole investigation, please download this file.
This is all my own work and I would appreciate it if you did not copy it. Thank you.
The ABC Conjecture.pdf
This is all my own work and I would appreciate it if you did not copy it. Thank you.
The ABC Conjecture.pdf
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