MathDB

n^2(n^2 + 2)^2 , n^4(n^2 + 2)^2, in base n^2 +1, same digits

Source: 1989 Swedish Mathematical Competition p1

March 28, 2021

number theoryDigitsPerfect Square

Problem Statement

Let

n

be a positive integer. Prove that the numbers

n^2(n^2 + 2)^2

and

n^4(n^2 + 2)^2

are written in base

n^2 +1

with the same digits but in opposite order.