Let R be the relation on N such that aRb when a/b is an integer power of 2. Show the least element of an equivalance class is odd.

Ok so I get its always a prime but how do I prove it.

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- Apr 16th 2011, 11:35 AMpoirotequivalence relation
Let R be the relation on N such that aRb when a/b is an integer power of 2. Show the least element of an equivalance class is odd.

Ok so I get its always a prime but how do I prove it. - Apr 16th 2011, 12:58 PMTinyboss
Let n be the smallest representative of [n] (a smallest element exists by well-ordering). If n is even, then n=2m for some m<n, and then mRn, contradicting that n was the smallest representative of the class.