To obtain the summary of a number with up to 9 digits, you should write how many digits it has, then how many of those digits are odd, and finally how many are even. For example, the number 9103405 has 7 digits, 4 of which are odd and 3 are even, so its summary is 743.

a) Find a number whose summary is 523.

b) Find a number that is equal to its own summary.

c) For any number with up to 9 digits, we can calculate the summary of the summary of its summary. Show that this procedure always leads to the same result, regardless of the initial number.