Consider an ellipse fixed at the origin of the xy-plane having semi-major axis 4 and semi-minor axis 3. A congruent ellipse rolls over the first ellipse without slipping. Initially, they share a common major axis.
Find the locus of focus (the one nearer to the origin) of the rolling ellipse, and calculate the distance traveled by the focus in one revolution (around the fixed ellipse).
Below is an example of twin & reversible primes: (173313197, 173313199); and (791313371, 991313371) Find the smallest non trivial pair with similar features .
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