The ABC conjecture [La conjecture ABC].

The horizontal and vertical axes display respectively the integer numbers from 1 to N. Each disk display a couple of coprime numbers A (X axis) and B (Y axis):
The number C is the sum of A and B:
                    C = A+B
The function Radical(N) gives the product of the prime factors (with an exponent equals to 1) of N. For example:
                    N = 1960 = 23x51x72
                    Radical(1960) = 21x51x71 = 2x5x7 = 70

Then the following function is computed:
                    k(A,B,C) = ---------------------
The ABC conjecture states that k(A,B,C) is less than a certain constant (unknown, but greater than 1 and hopefully lesser than 2...) whatever the values of A and B.

The surface and the luminance of each disk are proportional to k(A,B,C).

For this picture, the numbers A and B belong to [1,N=20] giving birth to the following values:

See some tridimensional visualizations:

See some related pictures (including this one):

(CMAP28 WWW site: this page was created on 09/21/2012 and last updated on 09/06/2022 10:57:52 -CEST-)

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