Enigma 1434: Triangular triples
From New Scientist #2595, 17th March 2007
A triangular number is an integer that fits the formula n(n+1)/2; such as 1, 3, 6, 10, 15.
45 is not only a triangular number (9 × 10)/2, but also the product of three different factors (1 × 3 × 15) each of which is itself a triangular number.
But Harry, Tom and I don’t regard that as a satisfactory example since one of those factors is 1; so we have been looking for triangular numbers that are the product of three different factors each of which is a triangular number other than 1.
We have each found a different 3-digit triangular number that provides a solution. Of the factors we have used, one appears only in Harry’s solution and another only in Tom’s solution.
What are the three triangular factors of my solution?