The ABC conjecture [La conjecture ABC].

The horizontal and vertical axes display respectively the whole 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:
                                3  1  2
                    N = 1960 = 2 .5 .7
                                     1  1  1
                    Radical(1960) = 2 .5 .7  = 2.5.7 = 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=50] giving birth to the following values:

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