Tuesday, November 14, 2017

Fun with numbers

Power of a number

Any power number can be expressed as the difference of two squares.

22  =  22  -   02      ;  32  = 52  - 42
23 =  32  -  12       ; 3 = 62    - 32
24    =  52  -  32    ;  34  = 15-  122
25  =  92  -  72      ; 35  = 42- 392
26  = 172  - 152    ; 36  = 1232 - 1202
27  = 332  - 311 ;   3= 3662  -  3612

Any odd square cannot be expressed as the difference of two squares with root numbers whose difference cannot be even. Any even squares cannot be expressed as the difference of two squares with root numbers whose difference cannot be odd..