Re: how to solve the integer equation Abs[3^x-2^y]=1
- To: mathgroup at smc.vnet.net
- Subject: [mg103025] Re: how to solve the integer equation Abs[3^x-2^y]=1
- From: Bill Rowe <wjrowe at sbcglobal.net>
- Date: Fri, 4 Sep 2009 03:16:05 -0400 (EDT)
On 9/3/09 at 7:10 AM, a.dozy.boy at gmail.com (a boy) wrote:
>Does the equation |3^x-2^y|=1 give only 4 groups of solution? (x,y)=
>(0,1),
>(1,1), (1,2), (2,3)
>can anyone give any else solution? when the two integers x and y
>become bigger and bigger, is there a pair integer (x,y) to give a
>small value for |3^x-2^y|? Or else,how to prove the equation
>|3^x-2^y|=1having only 4 groups of integer solution?
It is easy to show there are more than the 4 pairs you give
above. Specifically,
In[3]:= FindInstance[
Abs[3 x^2 - 2 y^2] == 1 && x > 2, {x, y}, Integers]
Out[3]= {{x->9,y->11}}