MathDB

Concatenating powers

Source: Kyiv City MO 2024 Round 2, Problem 10.1

February 4, 2024

number theoryDigits

Problem Statement

For some positive integer

n

, Katya wrote on the board next to each other numbers

2^n

and

14^n

(in this order), thus forming a new number

A

. Can the number

A - 1

be prime?
Proposed by Oleksii Masalitin