Let a be a prime of the form (2n+1), and let b be a prime of the form (2a+1), such that 1/b has an even period of length 2a, i.e. 0 followed by 2a decimal digits.

The 'splitadd' function splits these 2a digits into equal halves and adds them.

To give an (imaginary) example, say 1/b was 0.0123456789, then 'splitadd' would produce 01234+56789, and add these for a value of 58023.

Show that the result of the 'splitadd' function is always (10^a-1), or find a counterexample.