Pasted

sage: p = 17
sage: f = lambda x: (x^2 + x + 5) % p
sage: F = lambda S: {f(x) for x in S}
sage: {i for i in range(p)}
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
sage: F(_)
{0, 1, 5, 7, 8, 9, 10, 11, 13}
sage: F(_)
{0, 1, 5, 7, 9, 10, 13}
sage: F(_)
{0, 1, 5, 7, 10, 13}
sage: F(_)
{0, 1, 5, 7, 10, 13}
sage: 
sage: f = lambda x: (x^2 + 2*x + 5) % p
sage: F = lambda S: {f(x) for x in S}
sage: {i for i in range(p)}
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
sage: F(_)
{0, 2, 3, 4, 5, 6, 8, 12, 13}
sage: F(_)
{0, 2, 3, 5, 6, 12, 13}
sage: F(_)
{2, 3, 5, 6, 13}
sage: F(_)
{2, 3, 6, 13}
sage: F(_)
{2, 3, 13}
sage: F(_)
{3, 13}
sage: F(_)
{3, 13}
sage: