• Korean Journal of Mathematics
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• v.30 no.3
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• pp.433-442
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• 2022

Let N^(q) be an arithmetic table of a negative exponent polynomial with q-commuting variables. We study sequential properties of diagonal sums of N^(q). We first device a q-coefficient table $\hat{N}$ of N^(q), find sequences of diagonal sums over $\hat{N}$, and then retrieve the findings of $\hat{N}$ to N^(q). We also explore recurrence rules of s-slope diagonal sums of N^(q) with various s and q.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.1-15
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• 2020

In this work we investigate interrelationships between two arithmetic tables of (cx² + x + 1)^±m. It would give a way to expand (cx²+x+1)^-m by means of the coefficients of (x²+x+1)^m.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.191-203
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• 2020

Any powers of 11 are easily obtained from the Pascal triangle. In this work we study powering and negative powering of any k digit integers by means of certain arithmetic tables.