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Let N be the largest integer whose square has exactly 3 digits when written in base 9.

What is N, expressed in base 9?

 Jan 14, 2019
 #1
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\(\text{The largest 3 digit base 9 number is }9^3-1=728_d\\ \text{The largest perfect square less than this is }676_d=26_d^2\\ 676_d = 831_9\)

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 Jan 14, 2019

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