IMO Shortlist 2003 problem N2


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2. travnja 2012.
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Each positive integer a is subjected to the following procedure, yielding the number d = d\left(a\right):

(a) The last digit of a is moved to the first position. The resulting number is called b.
(b) The number b is squared. The resulting number is called c.
(c) The first digit of c is moved to the last position. The resulting number is called d.

(All numbers are considered in the decimal system.) For instance, a = 2003 gives b = 3200, c = 10240000 and d = 02400001 = 2400001 = d\left(2003\right).

Find all integers a such that d\left( a\right) =a^2.
Izvor: Međunarodna matematička olimpijada, shortlist 2003