- From: "Hoogendoorn, Sander" <[EMAIL PROTECTED]>
-> But what if the mod M comes out to 1 on one of
-> the intermediate steps? Then 1^2 - 2 = -1
-> Then what? spike
-Then you will be stuck in a loop, same thing happens when the outcome is
- -2, -1, 0 and 2
This case never occurs. If M = 2^p - 1 where p is prime and p > 2,
then M == 7 (mod 12). By quadratic reciprocity, the
Jacobi symbol (3 over M) is -1, so 3 is not a square modulo M.
Therefore x^2 - 2 == 1 (mod M) has no solution.
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