Guest wrote:Guest wrote:Guest wrote:i personally doubt the ABC-conjecture is true for one inescapable reason: 1+B= [tex]9^{n}[/tex] always results in a value for C/ rad function >1

For what [tex]\beta > 1[/tex], is [tex]9^{n} / rad( 1 * (9^{n} - 1) * 9^{n})^{\beta} > 1?[/tex]

And are there infinitely many ABC-triples in total that satisfy the above question for all appropriate [tex]\beta[/tex] > 1?

Example:

The one ABC-triple, [tex](A = 1, B = 9^{5} -1, C = 9^{5})[/tex] satisfy our question when [tex]1 < \beta < 1.32354 (approximately)[/tex] according to the Wolfram Alpha Calculator.

Relevant Reference Links:

http://www.wolframalpha.com/input/?i=factor(9%5E5+-1)

http://www.wolframalpha.com/input/?i=9%5E5%2F(2+*+11+*+61*3)%5E%CE%B2+%3E+1

Please keep searching for more such ABC-triples since infinity is far bigger than any number imaginable.