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Printer's glitch (Posted on 2015-05-05) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
Hints/Tipsa special one ...............triviaAdy TZIDON2015-05-06 11:03:40
re: answerJer2015-05-06 10:20:05
answerBenny2015-05-06 01:21:35
Some ThoughtsPart (i)Jer2015-05-05 13:45:48
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