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 Neither 3 nor 6 (Posted on 2011-03-11)
0, 25, 2025, 13225…are squares that remain squares if every digit in the number defining them is augmented by 1.
Let's call them squarish numbers.

a. List two more samples of squarish numbers.
b. Prove that all such numbers are evenly divisible by 25.
c. Why are there neither 3-digit nor 6-digit squarish numbers?
d. Prove that between 10^k and 10^(k+1) there is at most one squarish number.

 See The Solution Submitted by Ady TZIDON No Rating

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 Subject Author Date re(3): Part a only (spoiler) Charlie 2011-03-14 17:38:34 re(2): Part a only (spoiler) Jer 2011-03-14 09:11:42 part b (not very elegant) Steve Herman 2011-03-13 15:59:37 re: Part a only (spoiler) Charlie 2011-03-11 16:32:42 re: Part a only (spoiler) Charlie 2011-03-11 13:54:36 Part a only (spoiler) Charlie 2011-03-11 13:42:19

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