Solving Simultaneous Equation

Are a and b integers?

2009-06-18 15:49:14 補充：
a^n - b^n = about 1.549492661*10^80
a^m - b^m = about 2.562076113*10^89

where m-n = 9.3,
a, m, n and b are positive,
a and b are between 0 and 10.
m and n are between 80 and 100.

The condition should include a,b,m and n are real numbers.

There are three equations with 4 variables, it is likely that:
1. there is no solutions; or
2. there are infinite sets of solutions.

By putting b=0, it is clear that a=9.8 and n=80.9;
It should be noted that for a=9.8 and n=80.9, b can take any value from 0 to around 7.5. The reason is 7.5^80.9 although is very big (6.2*10^70) is insignificant compared with 1.549492661*10^80. Since the question cannot specify exactly these numbers 1.549492661*10^80 and 2.562076113*10^89, there are already infinite number of b's that can satisfy the conditions and with a=9.8 and n=80.9.

Indeed these equations can be evaluated by using numerical estimation method. Some other combinations of numbers are:
n 80.9018489215444 a 9.79957520621171 b 8.96
n 81.4795024487293 a 9.72347297247198 b 9.64

2009-06-21 22:20:23 補充：
2009-06-20 18:39:25 補充

then how about
a^n - b^n = 213968256
a^(n+1) - b^(n+1) = 2355994566

可參考
http://hk.knowledge.yahoo.com/question/question?qid=7009062001829

are m and n ntegers?