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?
(In reply to
Direct approach by Charlie)
So according to you Charlie, x = 43 in case of De Morgan and x = 45 in case of Jim.
It is also posible that x = 44 (in case of Jim), whereas x remaining the same for De Morgan.