Talk:First perfect square in base n with n unique digits: Difference between revisions
Talk:First perfect square in base n with n unique digits (view source)
Revision as of 12:45, 25 May 2019
, 5 years ago→Space compression and proof ?: Why 10123456789abcdefg is the smallest candidate
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Base 17: 423F82GA9² == 101246A89CGFB357ED
:::The residuals base 16 are 1 4 9 16<br>0+1+...+15+16 -> 80 -> 8 therefore no 17 digit perfect square made from digits 0..g in base 17 so searching for one is pointless.<br>101246A89CGFB357ED -> 81 -> 9 therefore may be a perfect square, just as well since you say it is.<br>smallest possible number made repeating 1 is 10123456789abcdefg so you only need to verify that there is no perfect square between 10123456789abcdefg and 101246A89CGFB357ED which contains all the digits between 0 and g to prove that 101246A89CGFB357ED is the smallest.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 10:07, 24 May 2019 (UTC)
::::Note that adding a zero to a number doesn't change it's digital root so the repeated digit can not be zero so 10123456789abcdefg must be the smallest candidate--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 12:45, 25 May 2019 (UTC)
:::So digital root 9, I think, drawn from the dual-symmetry base 17 cycle for perfect squares of
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