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Question 437: Let p1 and p2 be two odd primes. Show that there is a prime q such that q is not in {p1,p2} and q divides the sum p1 + p2.
Answer by AnlytcPhil(1810)   (Show Source):
You can put this solution on YOUR website! Let p1 and p2 be two odd primes. Show that there is a prime q such that q is
not in {p1,p2} and q divides the sum p1 + p2
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Example to illustrate, not a proof: 3 and 5 are two odd primes. We have to
show that there is a prime q, not between 3 and 5 such that q divides 3+5, or
8. Such a prime is q = 2.
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The sum of two odd primes must be even, and since the smallest odd prime is 3,
the sum of any two odd primes must be greater than 2. We also know that 2 will
divide any even number, and 2 is never between two odd primes. Thus the
theorem is proved with q = 2
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Edwin
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