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Peter L. Montgomery
science forum Guru Wannabe

Joined: 01 May 2005
Posts: 181 Posted: Sat Jul 15, 2006 7:24 pm    Post subject: Re: Number Theory In article <30524459.1152932253418.JavaMail.jakarta@nitrogen.mathforum.org>
Danilo <danilorj@gmail.com> writes:
 Quote: Find all positive integers n so that 8n^3+36n^2+55n+23 is a perfect cube. Thanks.

sci.math.num-analysis is for topics related to
numerical analysis, which typically involve
approximations and floating point arithmetic.
sci.math is more general. There is also a homework group
but I forget its name.

This said, look at your cubic f(n) = 8*n^3 + 36*n^2 + 55*n + 23
(it's much easier to read equations when you space
in accordance with operator precedence).
If m^3 = f(n), then m = f(n)^(1/3).
Since f(n) is about 8*n^3 for large n, m is about 2*n.
Find a better approximation for m when n is large.
Look for the needed conditions to make both m and n integers.
Do small values of n by a brute search, if needed.

--
Why do storms (e.g., Katrina) have human names,
while earthquakes (e.g., Loma Prieta) have place names?

pmontgom@cwi.nl Microsoft Research and CWI Home: Bellevue, WA Danilo
science forum beginner

Joined: 26 Mar 2006
Posts: 12 Posted: Sat Jul 15, 2006 2:57 am    Post subject: Number Theory Find all positive integers n so that 8n^3+36n^2+55n+23 is a perfect cube.
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