1. Let A be 1 more than the product of the primes 3, 5, and 7. Factor A into a product of primes and check how many of 3, 5,7 are factors of A.
2. Make a list consisting of a few of your favorite primes and let B be 1 more than the product of these primes. Factor B into a product of primes and check how many of the primes on your list are factors of B.
2. Primes [2 marks] A prim e p > 1 has no factors other than 1, so p%m 0 for all m є {2.3, p-1). Test all the integers greater than 1 that you can, and identify the primes (again, write your own code). How far can you get in 10 minutes (use a clock or watch to approximately time this)? Print (or write) the last three primes that you find, and also check them using a web tool (Google...
in the sieve of Eratosthenes for numbers less than 100, explain why after we cross our the multiples of 2 3 5 and 7 the remaining numbers are primes.
1. (Complex Multiplication) Let E : y x3 y23 to this congruence mod p. So for example, #E(Z3) = 3 because we have the solutions (0, 0), (1,0) and (2,0) and no more. - x. Then we can reduce E mod p to get mod p for various primes p. We write #E(Z») for the number of solutions This particular equation has some miraculous explore here patterns we (a) Make a chart that lists p, #E(Zp), and #E(Z) - p...
Let 1 3 -5-3 -1 -58 4 4 2 -5-7 (a) Using Gaussian elimination, find an LU decomposition for A. You should explicitly list every row operation you perform, perform individual row operations. -3 (b) Let b- Use your LU decomposition to solve Ax b.
Let 1 3 -5-3 -1 -58 4 4 2 -5-7 (a) Using Gaussian elimination, find an LU decomposition for A. You should explicitly list every row operation you perform, perform individual row operations.
-3 (b)...
1. Construct a DFSM to accept the language: L w E ab): w contains at least 3 as and no more than 3 bs) 2. Let E (acgt and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg. ge. Construct both a DFSM to accept the language and a regular expression that represents the language. 3. Let ab. For a string w E , let w denote the string w with the...
r-(003,0340 2. Let X-1,2,3, 4, 5,6) and let G (1), (123), (132), (45), (123) (45), (132) (45)). Let G act on X in the obvious way. (a) For eachx X and g E G, find Ox, G and Xg. Label these clearly. (b) Verify the orbit-stabilizer theorem and Burnside's lemma for this example and explain (i.e., demonstrate that you know what these are and mean). c) To thank your professors for doing such an amazing job all semester, you decide...
Molecular Species Lists List #1 1. NO2 6. IF3 2. PCI3 7. C2H6O (more than one possible isomer) NO3 3. C4H4 (all carbon atoms in a ring) 8. 4. HCN 5. PCI5 List #2 1. CH3BR 5. SbCls IC12* 2. 6. So,- 3. NO2* 7. ICI4 4. BF3 8. C2H2Cl2 (more than one possible isomer) 40 List #3 O3 (not a cyclic structure) PCl 1. 6. 2. H2NNH2 7. CIFS C3H6 (more than one possible isomer) CS2 8. 3. ВСЬ...
7. Product-cost subsidiration means that A) when one product is overcasted, it results in more than one other products overcasted when company underests more than one of its products, it will overcost more than one of its other products when a company undercosts one of its products, it will overcost at least one of its other products D) when one product is overcosted it results in all other products being overcosted 8. Refining a cost system involves which of the...
JAVA (programing) 1. For a given positive integer n, output the first n primes. E.g. n=3, output: 2,3,5; n=7, output: 2,3,5,7,11,13,17. 2. For a given integer n>1, list all primes not exceeding n. E.g. n=10, output: 2,3,5,7; n=16, output: 2,3,5,7,11,13. 3.For a given integer n>1, output its prime factorization. E.g. n=8, output: 2^3; n=72, output: 2^3*3^2.
8. Let S = classes? 1, 2, 3, 4, 5, 6, 7, 8). How many equivalence relations on S have exactly 3 equivalence
8. Let S = classes? 1, 2, 3, 4, 5, 6, 7, 8). How many equivalence relations on S have exactly 3 equivalence