MathDB

Each positive integer

a

undergoes the following procedure in order to obtain the number

d = d\left(a\right)

:
(i) move the last digit of

a

to the first position to obtain the numb er

b

; (ii) square

b

to obtain the number

c

; (iii) move the first digit of

c

to the end to obtain the number

d

.
(All the numbers in the problem are considered to be represented in base

10

.) For example, for

a=2003

, we get

b=3200

c=10240000

, and

d = 02400001 = 2400001 = d(2003)

.)
Find all numbers

a

for which

d\left( a\right) =a^2

.
Proposed by Zoran Sunic, USA

Problem Statement