About 10 years ago I published “My house's number” based on a peculiar property of 2592: 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.

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Posted by CodyDunning on 2023-08-25 02:26:19