Example
Taking p = 11 and a = 7, the relevant sequence of integers is
- 7, 14, 21, 28, 35.
After reduction modulo 11, this sequence becomes
- 7, 3, 10, 6, 2.
Three of these integers are larger than 11/2 (namely 6, 7 and 10), so n = 3. Correspondingly Gauss's lemma predicts that
This is indeed correct, because 7 is not a quadratic residue modulo 11.
The above sequence of residues
- 7, 3, 10, 6, 2
may also be written
- -4, 3, -1, -5, 2.
In this form, the integers larger than 11/2 appear as negative numbers. It is also apparent that the absolute values of the residues are a permutation of the residues
- 1, 2, 3, 4, 5.
Read more about this topic: Gauss's Lemma (number Theory)
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