Same-Digits Equality Expressions Generator
Created by Inder J. Taneja
Find signed sums of numbers equal to the signed sums of powers formed by splitting off their last digits.
Search options
For example, 123 becomes 12³. Each term uses the same sign on both sides. “2 operations” means three terms joined by two signs. Choose positive sums, plus/minus between terms, or include a negative first term.
Numbers used chooses the building blocks: from 10 to 120 means each term can be 10, 11, …, 120, including repeats. Final value chooses the answer: from 10 to 150 shows only equalities whose common value lies in that interval. In automatic mode, the final-value upper limit also expands the candidate numbers. Manual mode searches only the chosen numbers.
Example: with three terms from 10 to 120 and final value from 10 to 150, the generator may show 66 := 1^0 + 1^3 + 4^3 = 10 + 13 + 43.
Automatic search supports 2 operations up to 10,000 and 3 operations up to 500. Searches at the upper limits can take time. For larger 3-operation intervals or 4–5 operations, select the manual number interval.
Ready.
Results
Terms are ordered from smallest to largest so rearrangements are shown once. Every matching sign pattern is retained in “All solutions.” The selected one-per-value or all-solutions setting applies to both the screen and downloads; the screen count is a separate display limit.
References
This generator is based on the author’s following research works:
- Inder J. Taneja, Same Digits Equalities Expressions, Zenodo, February 19, 2019, pp. 1–182. doi:10.5281/zenodo.2573194.
- Inder J. Taneja, Same Digits Equality Expressions: Power and Plus, Zenodo, January 3, 2020, pp. 1–1729. doi:10.5281/zenodo.3597506.
- Inder J. Taneja, Same Digits Equality Expressions, WordPress, February 23, 2017. Read the article.