Re: Number theory assertion
- From: quasi <quasi@xxxxxxxx>
- Date: Sat, 27 May 2006 16:28:48 -0400
On 27 May 2006 13:12:39 -0700, "Deep" <deepkdeb@xxxxxxxxx> wrote:
Kindly consider the following two equations under the given conditions.
A^1/2 + B^1/2 = u^k (1)
A^1/2 - B^1/2 = v^k (2)
Given conditions: A, B are integers each > 1 , none is a perfect square
and (A,B)=1.
Odd k > 3 and (uv) is an integer > 1.
Assertion: u, v must assume values of the forms (3) and (4) where E >
F>1 and none is a perfect square.
u = E^1/2 + F^1/2 (3)
v = E^1/2 - F^1/2 (4)
Any comment upon the correctness of the assertion will be appreciated.
Question: I can see why you exclude k=1 but why do you exclude k=3?
quasi
.
- References:
- Number theory assertion
- From: Deep
- Number theory assertion
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