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Our Ages

Age 14 to 16 Challenge Level:

Many thanks to Robert Simons for this question:

"I am exactly $n$ times my daughter's age. In $m$ years I shall be exactly $(n-1)$ times her age. In $m^2$ years I shall be exactly $(n-2)$ times her age. After that I shall never again be an exact multiple of her age. Ages, $n$ and $m$ are all whole numbers. How old am I?

Now suppose there is some wishful thinking in the above assertion and I have to admit to being older, and indeed that I will be an exact multiple of her age in $m^3$ years. How old does this make me?"