**2592=2^5*9^2.**

There are additional numbers fitting the definition below:

a. The number is a positive integer of more than 1 digit.

b. Its value remains unchanged if some of the operations **^,***
are introduced between its digits.

c. Absence of any of the above signs between 2 adjacent digits signifies their concatenation.

d. Leading zeroes within an exponent are allowed.

e. Brackets may be added to define the order of operations.

Examples:

34425=3^4*425=81*425=34425;

9509900499 = 95^0*99^004*99.

(i)Prove that there is infinite number of "printer's glitch" numbers.

(ii) List all such numbers below **
400,000. **