Some equations with features of digit reversal and powers

2016/02/19 by Geoffrey B. Campbell, Campbell, Geoffrey B., Aleksander Zujev +1
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1602.06320

Abstract

In this paper we consider integers in base 10 like abc, where a, b, c are digits of the integer, such that abc² - (abc ⋅ cba) = ± n², where n is a positive integer, as well as equations abc² - (abc ⋅ cba) = ± n³, and abc³ - (abc ⋅ cba) = ± n² We consider asymptotic density of solutions. We also compare the results with ones with bases different from 10.

Related

• Squares with three nonzero digits
• Digit Reversal Without Apology
• On the binary digits of n and n²
• The joint distribution of binary and ternary digits sums
• On finding all positive integers a,b such that b\± a and ab are\n palindromic