![]() It has been conjectured that each natural number not equal to 216 can be written in the form p + T x, where p is 0 or a prime, and T x = x( x+1)/2 is a triangular number. ![]() ![]() But since there is no way to express it as the sum of the proper divisors of any other integer, it is an untouchable number. It is also the sum of a twin prime (107 + 109). Since 216 = 3 3 + 4 3 + 5 3 = 6 3, it is the smallest cube that is also the sum of three cubes ( Plato was among the first to notice this, and mentioned it in Book VIII of Republic).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |