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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

Comments: ( Back to comment list | You must be logged in to post comments.)
 part 1b. (spoiler) | Comment 4 of 11 |
(In reply to part 1a (spoiler) by Charlie)

1169  881  431              120           41

meaning

(1169/120)^2 - (881/120)^2 = (881/120)^2 - (431/120)^2 = 41

 Posted by Charlie on 2013-03-26 08:46:42

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