ASU 244 All Soviet Union MO 1977 2 perfect squares create a fine number
Source:
July 6, 2019
Perfect Squarenumber theory
Problem Statement
Let us call "fine" the -digit number if it is exact square itself and the two numbers represented by its first digits (first digit may not be zero) and last digits (first digit may be zero, but it may not be zero itself) are exact squares also. a) Find all two- and four-digit fine numbers. b) Is there any six-digit fine number? c) Prove that there exists -digit fine number. d) Prove that there exist at least ten -digit fine numbers. e) Prove that there exists -digit fine number.