1)How many number of squares are there in Zp,for p not equalto 2?
2) If p is a relation on a set S,what is symmetric &transsitive on S,does there is a partition corresponding to p?
3)f is an entire function which misses one point.what can you say about the point?
2006-06-30 23:07:30 · 2 answers · asked by sarkar_sumitra_bir 1 in Science & Mathematics ➔ Mathematics
I just took an abstract class and I have forgotten everything
2006-07-01 08:52:23 · answer #1 · answered by theFo0t 3 · 0⤊ 0⤋
For question 1, this is basically how many elements in Zp are residues.
We have 0^2 = 0, and for any non-zero element, if x^2 = y, then (-x)^2 = y, so these numbers have the same square.
And, if x^2 = y^2 mod p, p|(x-y)(x+y) if x is not y, then P can't divide x-y, so p | x+y, which means y = -x, mod p.
Thus, two distinct elements x,y have the same square mod p iff x = -y. Thus, there are (p-1)/2 squares if you do not include 0, (p+1)/2 if you do count 0.
2006-07-04 02:40:30 · answer #2 · answered by fatal_flaw_death 3 · 0⤊ 0⤋