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Modular Arithmetic Calculator Field Guide: When Five Operations, One Bezout Identity, and the Bit-Length Rule Decide Whether Your Modular Computation Is Exact or a Free Estimate

Modular arithmetic field guide: five operations (add, subtract, multiply, inverse, power) with BigInt precision up to 10^18. Walks through the extended Euclidean algorithm for inverse, square-and-multiply for power, and the canonical [0, m-1] representative.

Contingency Table Chi-Square, Fisher Exact, and Cramér’s V Tutor: A Field Guide to Hypothesis Testing When Cells Are Small, Categories Are Many, and ‘Significant’ Is Only Half the Story

When Pearson chi-square, Yates continuity correction, the G likelihood-ratio test, and Fisher's exact test all answer the same question with different assumptions, you need more than a single number to make a defensible inference. This field guide walks through the eight decisions — test choice, Yates vs no-Yates, Fisher for small samples, G as likelihood ratio, effect sizes via Cramer V / phi / C, adjusted residuals with BH-FDR multiplicity, Cochran expected-count rule, and Chapman capture-recapture on 2x2 mark-recapture tables — that the Contingency Table Chi-Square, Fisher Exact, and Cramer V Tutor surfaces side by side on every 2x2 or RxC table you paste in.