List all positive integers such that deleting their first digit is equal to dividing the number by 25.

Let the number be n digits long, with a body of b (length n-1) and an initial digit of a.

Then a*10^N-1 + b = 25b

b = a*10^n-1 / 24 = 125*(a/3)*10^(n-4)

In order for b to be an integer, a must be a multiple of 3. and n must be at least 4.

So a can be 3, 6, or 9.

Each leads directly to a solution

The full number = 3125*10^k or 6250*10^k or 9375*10^k