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Thabit ibn Qurra (circa 850 A.D.) noted that if n>1 and each of p = 3*2^(n-1) - 1, q = 3*2^n - 1, and r =(p+1)*(q+1) - 1 is prime, then (2^n*p*q) and (2^n*r) are amicable pairs. Descartes wrote to Mersenne in 1638 with the pair 9363584 and 9437056 (n = 7).

 

  Submitted: 1999-09-02 18:40:00;   Last Modified: 2009-03-28 21:34:15.



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