Tag Archives: numbers

An apparition of Mordell

Consider the equation: where is a positive integer 1, 2, 3… For a given , will the above equation have integer solutions and, if yes, what are they and how many? We have heard of accounts of people receiving solutions … Continue reading

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A layman’s overview of the arithmetic of encryption

Life as an encryption-decryption cycle Encryption is a concept as old as life itself. The sequence of proteins, the primary purveyors of function in life as we know it, is encrypted within nucleic acids. It is decrypted by this remarkable … Continue reading

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Division-multiplication parabolas, triplications, and quadratic residues

Introduction Many strands of our investigations on conic-generating integer sequences, word fractals and cellular automaton models for pattern formation came together in an unexpected manner while investigating a simple integer sequence. While some of these connections have have been known … Continue reading

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The mean hyperbola and other mean functions

Let be two numbers such that, We use to construct a specific rectangular hyperbola using one of the following methods: Method-I (Figure 1: this is based on an approach we described earlier) Figure 1 1) Mark point , which will … Continue reading

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The geometric principles behind discrete dynamical systems based on the generalized Witch of Agnesi

Consider the family of curves defined by the equation following parametric equation , where and It defines a family of probability distribution functions (PDFs): This can be seen from the above equations because Figure 1 Examples of these PDFs are … Continue reading

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Reflections on our journey through the aliquot sums and sequences

The numerology of aliquot sums and perfect numbers The numerology of the Pythagorean sages among the old yavana-s is one of the foundations of science and mathematics as we know it. One remarkable class of numbers which they discovered were … Continue reading

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Residues of squares, sequence curiosities and parabolas galore

Squares and their residues This is an exploration of number triangles in the same vein as some other such we have previously described . It resulted in some observations that seemed interesting to us. Some are perhaps trivial but some … Continue reading

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