The structure of even powers in Z 3 : Critical structural factors that prevent the formation of even-powered triples greater than squares

J Leyendekkers, A Shannon
2011 NNTDM   unpublished
Integer structure analysis illustrates the critical structural factors which underpin the failure of (N 4 m +M 4 m) ever to equal an equivalent power. The number 3 plays a vital role as integers divisible by 3, when raised to an even power of the form 4m, have rows in a table of modular rings which are triangular numbers, whereas other integers raised to the same power have rows which are pentagonal numbers. The substructure within these sequences of penta-gonal numbers is order within order,
more » ... der within order, analogous to structure in chaos theory.