A businessman needs to send an urgent quotation to his business partner, who has gone out of town for a family function. The quotation can be sent only by post but the businessman is worried about corporate espionage. Hence, he decides to send the quotation through a figure which he and his partner used to use when they batchmates in college.
He uses a triangle with vertices marked with three unknown integers: X, Y and Z. The edges have some number written on them. Each vertex is related to its adjoining numbers in the same manner. The two smaller numbers among X, Y and Z are perfect squares and their sum is equal to the largest number (which is twice a perfect square). Now, these three obtained values are divided by a perfect square and the same relationship still holds. These values obtained are the final values of X, Y and Z.
From past experience, his partner knows that the quotation is formed by arranging all the digits of X, Y and Z in descending order. Also, the quotation is the smallest seven-digit number thus formed.
What is the quotation that the businessman wants to send to his partner?