Application of diophantine equations for practical problems solution in biology

Sergey P Klykov*

An attempt was made to use the Diophantine equations for the analysis of S-shaped curves of the growth of microorganisms. The most famous of such equations are the equation of the Pythagorean Theorem and the equation of Fermat’s Last Theorem, FLT. The article does not claim to prove FLT, but it shows interesting facts for biological objects - there are cells of microorganisms that are growing according to the S-shaped growth curve.  It was shown by using of an elementary algebra that the solution of the equation an + bn = cn cannot simultaneously have three integer nonzero roots “a”, “b” and “c” for integers n> 2. It was shown, that the same unsolvable situation can accompany the analysis if n = 2. Last case occurs due to the fact that the irreducible complexity containing the major, Φ, and minor, φ, numbers is always preserved for pairs of numbers with “a” and “c”, or with “b” and “c”. An attempt of practical application in biology of the found patterns were shown as a hypothesis, which has a fairly plausible explanation using the models used for the analysis in this paper.

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Published on: May 26, 2021 Pages: 13-16

Full Text PDF Full Text HTML DOI: 10.17352/ojb.000019
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