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Digit Increments 2 (Posted on 2024-04-15)

For which digits d, is it possible to add d to every digit of a square and get another square?
For example, adding 3 to each digit of 16 gives 49.However, adding zero to each digit in this manner is NOT permissible.

For which digits d are there infinitely many such squares?

*** Digit sums greater than 9 are not allowed. For example, you could not add 8 to the digits of 81 to get 169.

Submitted by K Sengupta

Rating: 5.0000 (2 votes)

Solution: (Hide)

The values of d for which the given conditions are met are therefore: 1,3,5, and 8.
It appears that d=3 can have infinite solutions. The square of a sting of k 3s followed by a 4 is transformed by d=3 into The square of a sting of k 6s followed by a 7.
For an explanation, refer to:
The solution submitted by Charlie in this location.
The solution submitted by Larry in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: computer solution	Math Man	2024-04-16 15:02:27
Computer solution	Larry	2024-04-15 09:47:09
computer solution	Charlie	2024-04-15 08:56:59

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