Let T be the set of triangular numbers and T* be the set of all products of any two triangular numbers. Show that:

1. Among elements of T, each of the digits 0,1,5 and 6 occur in the units place twice as frequently as each of the digits 3 and 8. (More precisely, if MBk is the set of elements of T that are less than B and end in k, then, e.g., MB1/MB8 approaches 2 as B approaches infinity.)

2. None of the elements of T* end in 2 or 7.