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initial version

Given that (n+p)=n2 mod p, you just have to compute the numbers n2modp for all integers between 0 and p1. If you want to avoid repetitions, you just have to put them in a set. Here is how:

sage: p = 17
sage: S = {n^2 % p for n in range(p)}
sage: S
{0, 1, 2, 4, 8, 9, 13, 15, 16}

sage: p = 123457
sage: S = {n^2 % p for n in range(p)}
sage: len(S)
61729
click to hide/show revision 2
No.2 Revision

Given that (n+p)=n2 mod p, you just have to compute the numbers $n^2 { \mbox{ mod } pforallintegersbetween0andp-1$. If you want to avoid repetitions, you just have to put them in a set. Here is how:

sage: p = 17
sage: S = {n^2 % p for n in range(p)}
sage: S
{0, 1, 2, 4, 8, 9, 13, 15, 16}

sage: p = 123457
sage: S = {n^2 % p for n in range(p)}
sage: len(S)
61729
click to hide/show revision 3
No.3 Revision

Given that $(n + p) p)^2 = n^2 + 2np + p^2 = n^2 \mbox{ mod } p,youjusthavetocomputethenumbersn^2 \mbox{ mod } pforallintegersbetween0andp-1$. If you want to avoid repetitions, you just have to put them in a set. Here is how:

sage: p = 17
sage: S = {n^2 % p for n in range(p)}
sage: S
{0, 1, 2, 4, 8, 9, 13, 15, 16}

sage: p = 123457
sage: S = {n^2 % p for n in range(p)}
sage: len(S)
61729