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A Perplexing (Prime) Puzzle (Posted on 2007-06-05) Difficulty: 4 of 5
Consider the quadruplets (p,q,r,s) of positive integers with p>q>r>s, and satisfying pr+qs= (q+s+p-r)(q+s-p+r).

Is it ever the case that pq+rs is a prime number?

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (3 votes)

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Hints/Tips Hint | Comment 4 of 5 |
(In reply to Helpful Observation? by Tommy)

At the outset, assume that (pq+rs) is prime.

Write, pq+rs = (p+s)r + (q-r)p = = t*gcd(p+s, q-r), where t is a positive integer as each of p, q, r and s are positive.

Thus, either t = 1, or gcd(p+s, q-r) = 1(why?)

Examine the two cases

Edited on June 29, 2007, 12:57 pm
  Posted by K Sengupta on 2007-06-29 12:52:26

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