SOLUTION: For arbitrary positive integers k, m, and n, will there exist a prime p such that {{{abs(1/m

SOLUTION: For arbitrary positive integers k, m, and n, will there exist a prime p such that {{{abs(1/m - n/p) <= k/2^p}}}?

Question 1183795: For arbitrary positive integers k, m, and n, will there exist a prime p such that ?
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

No, because m=1, n=1, k=1, is a counter-example.  To show that, we substitute



That only holds when p=1, but 1 is not a prime.

It does not work for the first prime 2




And as p increases through larger and larger primes, the left side increases
approaching 1, but the right side decreases approaching 0.  So no larger
integer for p can possibly be a solution, let alone a larger prime number.

Edwin

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