It is remarkable that the equation | x^2 | = 2 has no rational solution. But it has a solution in a finite field. I think the old Pythagorean would like the result. Today's mathematics faculties probably don't attach any further importance to the result.

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Here is the way I found this sequence independent from the handbook. Order the numbers in the Galois field G(p) symmetrically to zero. One half is denoted as positive numbers, the other as negative. If a is a positive number in this field, then the equation
| x^2 | = a has always a solution if p is a Sophie Germain prime.

Details can be found in my essay, will be published if time permits it.

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p is prime and 2p+1 is also prime. I just learned from the "The Handbook of Integer Sequences" ( https://oeis.org ) these are Sophie Germain primes.

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