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#1 2007-02-20 10:28:11
- Stanley_Marsh
- Member
- Registered: 2006-12-13
- Posts: 345
Help
When is 1+x^1+x^2+x^3........x^m=y^n for x,y,m,n>=3
for example 1+3+3^2+...3^4=11^2
I try everything I can think of , stilll hehe
Numbers are the essence of the Universe
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#2 2007-02-20 11:12:49
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Help
I may be mistaken, but it looks like you may just have to try values and see which ones work. I don't see how you'd do this algebraically.
However, you can change the left-hand expression into something a bit easier to handle.
So, for your example, 1+3+3^2+3^3+3^4 = (3^5 - 1)/(3-1) = 121 = 11².
That might help you try out various values quicker because it would be easier to calculate the summation.
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It wanted to be normal.
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