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 Conga Primes (Posted on 2013-03-23)

x^2-y^2 = y^2-z^2 = 5 is a classic problem that can be solved in the rationals, with, e.g.:

(49/12)2-(41/12)2 = (41/12)2-(31/12)2 = 5 (Fibonacci).

We seek non-trivial rational solutions to x^2-y^2 = y^2-z^2 = P, with P prime. Since we can always find compound multiples of such solutions with other primes happily joining the chain, let's call these paragons 'conga primes'. (Conversely, primes that only appear in conjunction with other primes could be 'tango primes', since it takes at least two...)

1. Solve over the rationals:
x^2-y^2 = y^2-z^2 = 7
x^2-y^2 = y^2-z^2 = 41

2. Give an example of a 'conga prime', P, greater than 41, such that x^2-y^2 = y^2-z^2 = P.

 See The Solution Submitted by broll No Rating

 Subject Author Date re: still no luck on part 2 broll 2013-03-29 10:09:08 re(2): more results, but still no part 2 soln Charlie 2013-03-27 11:29:40 re: more results, but still no part 2 soln broll 2013-03-27 09:08:51 re: still no luck on part 2 broll 2013-03-27 08:02:19 re: still no luck on part 2 broll 2013-03-27 04:49:33 still no luck on part 2 Charlie 2013-03-26 14:21:36 more results, but still no part 2 soln Charlie 2013-03-26 09:25:24 part 1b. (spoiler) Charlie 2013-03-26 08:46:42 part 1a (spoiler) Charlie 2013-03-26 08:35:08 re: Are there solutions? broll 2013-03-26 01:11:09 Are there solutions? Jer 2013-03-25 22:08:49

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