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Topic: concatenation equation (Read 755 times) |
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Benny
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concatenation equation
« on: Feb 24th, 2008, 12:30am » |
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72^2_27^2 = 2277^2. (5184_729 = 5184729)
Let _ be the concatenation equation representation.
72^2 = 5184
27^2 = 729
2277^2 = 5184729
Are there integers a, b, and k such that (a^k_b^k)^(1/k) is an integer, for k>2?
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If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
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Barukh
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Re: concatenation equation
« Reply #1 on: Feb 24th, 2008, 4:36am » |
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You mean are there other solutions?
Yes. b = 3, for instance.
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| « Last Edit: Feb 24th, 2008, 9:26am by Barukh » |
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towr
wu::riddles Moderator
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Re: concatenation equation
« Reply #2 on: Feb 24th, 2008, 11:05am » |
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I haven't had any luck finding solutions with k > 2..
Plenty more solutions with k=2 though.
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Wikipedia, Google, Mathworld, Integer sequence DB
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Benny
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Re: concatenation equation
« Reply #3 on: Feb 24th, 2008, 11:35am » |
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Me neither. I'm still trying to figure out this problem.
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If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
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