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Topic: number of form m^n (Read 1871 times) |
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inexorable
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number of form m^n
« on: May 18th, 2011, 7:38pm » |
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give an algorithm to find if a given integer is of the form m^n where m >1 and n >1
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towr
wu::riddles Moderator
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Re: number of form m^n
« Reply #1 on: May 18th, 2011, 10:39pm » |
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x = ln(m**n)
for (i = 2; i <= x/ln(2); i++)
{
y = round(exp(x/i));
if(y**i == m**n)
print y,i;
}
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| « Last Edit: May 18th, 2011, 10:44pm by towr » |
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singhar
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Re: number of form m^n
« Reply #2 on: Jul 6th, 2011, 11:19am » |
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@tower, Could you explain what is this algo doing:
I was thinking of finding the prime factors below sqrt(N) and then finding how many times each one of them repeats..
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towr
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Re: number of form m^n
« Reply #3 on: Jul 6th, 2011, 11:44am » |
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I'm searching for possible exponents in that algorithm. The largest exponent would be when m=2, and is ln(x)/ln(2). So I can just search for the few possible exponent between 2 and ln(x)/ln(2).
Basically I exploit the identity: x = mn <=> ln(x) = n*ln(m)
However, if you can use floating point arithmetic thing will get much trickier.
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Dufus
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Re: number of form m^n
« Reply #4 on: Dec 25th, 2011, 9:06pm » |
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I think doing a binary search for N would do here. That would take O(LogN) time.
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towr
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Re: number of form m^n
« Reply #5 on: Dec 26th, 2011, 12:11am » |
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I don't see how that could possibly work. Bear in mind that you don't know m. There's nothing to tell you whether some candidate you tried is greater or smaller than the real n you're after.
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