MathDB
Can the digits of 16^n be nonincreasing

Source: XI Olimpíada Matemática del Cono Sur (2000)

July 26, 2011
number theory unsolvednumber theory

Problem Statement

Call a positive integer descending if, reading left to right, each of its digits (other than its leftmost) is less than or equal to the previous digit. For example, 42214221 and 751751 are descending while 476476 and 455455 are not descending. Determine whether there exists a positive integer nn for which 16n16^n is descending.