- #1
nomadreid
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- Homework Statement
- prove or disprove: for every real nonzero a & positive integers n,m: n^ia does not end up at the same angle (modulo full rotations) as m^ia.
- Relevant Equations
- obviously the relations between the exponential function and the natural log, and the periodicity, and that e^iA gives A in radians, and so forth. What else, I'm not sure -- maybe transcendental number properties; this is not really a homework problem, but since it has the same form as one and is probably something easy , I thought this might be the most appropriate place to post.
reducing it to various forms: for example, the one in the title, or 2*pi*k(ln m) = a(ln(n/m)), and so forth. My gut feeling is that it is true (that no such foursome exists), but manipulations have not got me anywhere. Anyone push me in the right direction? I am probably overlooking something trivial, no?