4 slides/page
... • Subset: A ⊂ B if every element of A is an element of B ◦ Note: Lots of people (including me, but not the authors of the text) usually write A ⊂ B only if A is a strict or proper subset of B (i.e., A 6= B). I write A ⊆ B if A = B is possible. ...
... • Subset: A ⊂ B if every element of A is an element of B ◦ Note: Lots of people (including me, but not the authors of the text) usually write A ⊂ B only if A is a strict or proper subset of B (i.e., A 6= B). I write A ⊆ B if A = B is possible. ...
Algorithmentheorie 03
... Each odd prime number p divides 2p-1 – 1. Examples: p = 17, 216 – 1 = 65535 = 17 * 3855 p = 23, 222 – 1 = 4194303 = 23 * 182361 Simple primality test: 1 Calculate z = 2n-1 mod n 2 if z = 1 3 then n is possibly prime 4 else n is definitely not prime Advantage: This only takes polynomial time ...
... Each odd prime number p divides 2p-1 – 1. Examples: p = 17, 216 – 1 = 65535 = 17 * 3855 p = 23, 222 – 1 = 4194303 = 23 * 182361 Simple primality test: 1 Calculate z = 2n-1 mod n 2 if z = 1 3 then n is possibly prime 4 else n is definitely not prime Advantage: This only takes polynomial time ...
(pdf)
... Q[x] with 1 ≤ deg g(x), deg h(x) < m such that mα (x) = g(x)h(x). Since α is a root of mα (x), then 0 = mα (α) = g(α)h(α). This implies that either g(α) = 0 or h(α) = 0. However, both g(x) and h(x) have smaller degrees than mα (x), which contradicts the fact that mα is the smallest degree polynomial ...
... Q[x] with 1 ≤ deg g(x), deg h(x) < m such that mα (x) = g(x)h(x). Since α is a root of mα (x), then 0 = mα (α) = g(α)h(α). This implies that either g(α) = 0 or h(α) = 0. However, both g(x) and h(x) have smaller degrees than mα (x), which contradicts the fact that mα is the smallest degree polynomial ...
Slides Set 1 - faculty.cs.tamu.edu
... The second question concerning the testing of primality is simpler. If a number x is not prime, then it has a divisor d in the range 2<= d <= sqrt(x). Trial divisions are fast enough here! Simply check whether any number d in the range 2 <= d < 100 000 divides a 10-digit chunk of e. ...
... The second question concerning the testing of primality is simpler. If a number x is not prime, then it has a divisor d in the range 2<= d <= sqrt(x). Trial divisions are fast enough here! Simply check whether any number d in the range 2 <= d < 100 000 divides a 10-digit chunk of e. ...
