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| viXra.org > General Mathematics > viXra:2509.0126 |
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General Mathematics |
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Authors: Amit Kumar
The concept of combination is crucial to layout groundwork for many fundamental sciences, finance and technical domains. There are multiple known methods to show that the combination (binomial coefficient) is integral in nature. This article approaches the same concept with simple non-inductive algebraic steps that can be followed by a wide range of audiences. This article separates an ${n choose k}$ into mutually exclusive and collectively exhaustive cases and then shows for each case that any term in a denominator have at least one corresponding multiple in the numerator. All k for a particular n (for an ${n choose k}$) are visualized through plots to gain better understanding. In the context of the plots, this different way of looking at a Combination ${n choose k}$, gives hindsights into the generation process of factors and prime numbers contained within a particular range of 1 to n.
Comments: 16 Pages. Appendix and supplementary material can be obtained upon the request.
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[v1] 2025-09-23 17:24:26
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