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Twin prime equivalence

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  • Sebastian Martin Ruiz
    Hello all: Let p and q two distinct odd prime numbers. p and q are twin primes if and only if (p+q)/(p-q) is integer. -- trivial
    Message 1 of 1 , Feb 24, 2009
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      Hello all:
      Let p and q two distinct odd prime numbers.
      p and q are twin primes if and only if (p+q)/(p-q) is integer.


      --> trivial
      <-- A= (p+q)/(p-q) Integer  then A+1 is integer  A+1=2p/(p-q)let r prime r | (p-q) then r | 2p then r | p+q then r | 2q GCD(p,q)=1 then r=2then p-q=2^kif 4 | (p-q)  implies 4 | 2p and 4 | 2q y then 2 | p absurditythen p-q=2
      Sincerely
      Sebastian Martin Ruiz




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