Quadratic Reciprocity Taylor Dupuy
... case 3 Suppose n is not a square mod p. We need two facts. 1. (p − 1)! ≡ −1 mod p (which holds generally) 2. (p − 1)! ≡ n(p−1)/2 . (which holds when n is not a square) First, Z/p is Q a field. We write out (p − 1)! and pairing inverses and get (p − 1)! ≡ c∈F× c = −1, Since the only elements left ove ...
... case 3 Suppose n is not a square mod p. We need two facts. 1. (p − 1)! ≡ −1 mod p (which holds generally) 2. (p − 1)! ≡ n(p−1)/2 . (which holds when n is not a square) First, Z/p is Q a field. We write out (p − 1)! and pairing inverses and get (p − 1)! ≡ c∈F× c = −1, Since the only elements left ove ...
11-1
... Carlo uses a double-pan balance and three different weights to weigh bird seed. If his weights are 1 lb, 2 lb, and 5 lb, what whole pound amounts is he able to weigh? 1, 2, 3, 4, 5, 6, 7, and 8 lb ...
... Carlo uses a double-pan balance and three different weights to weigh bird seed. If his weights are 1 lb, 2 lb, and 5 lb, what whole pound amounts is he able to weigh? 1, 2, 3, 4, 5, 6, 7, and 8 lb ...
Linear Inequalities
... Notice that the parenthesis (“)”) means that x = −3 is not included in the solution set. You can also write solutions to inequalities using interval notation. In this case, the solution would be (−∞, −3). Notice that the “)” next to the “−3” matches the “)” on the picture. In interval notation, (rou ...
... Notice that the parenthesis (“)”) means that x = −3 is not included in the solution set. You can also write solutions to inequalities using interval notation. In this case, the solution would be (−∞, −3). Notice that the “)” next to the “−3” matches the “)” on the picture. In interval notation, (rou ...
VMC Math Tutorials
... fraction with a common denominator of 100. For example, instead of saying "8 out of every 100 professional basketball players are female," we can say "8% of professional basketball players are female." A percent can always be written as a decimal, and a decimal can be written as a percent, by moving ...
... fraction with a common denominator of 100. For example, instead of saying "8 out of every 100 professional basketball players are female," we can say "8% of professional basketball players are female." A percent can always be written as a decimal, and a decimal can be written as a percent, by moving ...
pi, fourier transform and ludolph van ceulen
... good evidence for 4(8/9)2 =3,16. The first theoretical calculation seems to have been carried out by Archimedes of Syracuse (287-212 BC). He used inscribed and circumscribed polygons. Applying a polygon with 96 side he obtained the approximation 3 10/71 < < 31/7 (3,1408<<3,1429). Archimedes did ...
... good evidence for 4(8/9)2 =3,16. The first theoretical calculation seems to have been carried out by Archimedes of Syracuse (287-212 BC). He used inscribed and circumscribed polygons. Applying a polygon with 96 side he obtained the approximation 3 10/71 < < 31/7 (3,1408<<3,1429). Archimedes did ...
