13 Feb
2010
13 Feb
'10
10:31 a.m.
I also find some more Bang's theorems: If all the faces of a tetrahedron have the same perimeter, then the faces are all congruent triangles. If the faces of a tetrahedron have equal areas then they are congruent. Or, I suspect perhaps of more interest to Prof. Guy: http://tinyurl.com/BangThmAmazon Paraphrasing: In the sequence a^n - 1 or a^n + 1, for fixed a>1 and variable n, every term has a prime factor that does not divide any previous term, except if a = 2 and n = 6 for the -1 case, and a = 2 and n = 3 for the +1 case. (Zsigmondy generalized this result to a^n - b^n and a^n + b^n, with the same exceptions). But in any case I don't find any further biographical information... --Joshua Zucker