Three
distinct 3-digit positive decimal (base 10) integers
P,
Q and
R, having no leading zeroes and with
P >
Q >
R, are such that:
(i)
P,
Q and
R (in this order) are in geometric sequence, and:
(ii)
P,
Q and
R are obtained from one another by
cyclic permutation of digits.
Find all possible triplet(s)
(P, Q, R) that satisfy the given conditions.
Note: While the solution may be trivial with the aid of a computer program, show how to derive it without one.
The other day, Jim excitedly told me, "Did you realise I will turn x years old in the year x^2?"
He wasn't the first to think of this. The 19th century mathematician August de Morgan used to used to boast that he was x years old in the year x^2. He died in 1871.
In what year was Jim born? When will his prediction be true? In what year was de Morgan born? What is x in each case?
Latest: 
Bonus: 
