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.numanalysis 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 
