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       ; 3³   = 6²    - 3²

2⁴    =  5²  -  3^{2    ;}  3⁴  = 15²  -  12²

2⁵  =  9²  -  7²      ; 3⁵  = 42²  - 39²

2⁶  = 17²  - 15²    ; 3⁶  = 123² - 120²

2⁷  = 33²  - 31^{1 ;}   3⁷  = 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..