2026-10-14T18:08:14Z https://www.scidb.cn/oai

10.57760/sciencedb.010pz 2026-09-07T09:30:55Z

2026-09-07 A Systematic Validation Dataset for the Analytical Formula of Power Differences doi:10.57760/sciencedb.010pz en This dataset systematically validates the lower difference formula for positive integer powers through a three-tier structure: full coverage of coprime pairs, non-coprime controls, and deep verification of 20 representative coprime pairs. For any integers A > 1, B > 1, the lower difference is defined as:Q = A^x - B^ywhere y = floor(x * log_B A), i.e., the exponent of the largest power of B not exceeding A^x. This lower difference has the equivalent analytical expression:Q = A^x * ( 1 - B^(-{x * log_B A}) )where {t} denotes the fractional part of t.The data cover all pairs with bases from 2 to 100 (both coprime and non-coprime) and deep verification for 20 representative coprime pairs (exponents up to 5000). All data points have zero error, confirming the formula is exact for any positive integer bases. Data files contain only four integer columns (A, B, x, y), compact and easy to download. power difference; exponential Diophantine equation; analytical formula; validation data; lower difference; base; exponent ceng fei ge PUBLIC https://creativecommons.org/licenses/by/4.0/ dataset Science Data Bank