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Explain what it means for a number a to be a pseudoprime to the base b. Show that 1387 is a pseudoprime to the base 2...
Show that 217 is a pseudoprime to the base 5 but is not a strong pseudoprime to the base 5.
just question 3 2. (9 marks) This question is about infinite series. (a) Explain what it means for an infinite series Σ a, to converge to the sum L E R. (b) For the series 2ー, write down a formula for the kth partial sun 5.- (c) Using your answers to parts (a) and (b), show that Σ n'tn-1. Hint for Part (b: what is T12 -1 91 nn+1 We were unable to transcribe this image 2. (9 marks) This...
(b) Prove that n is an odd pseudoprime number if and only if 2"-1-1 mod n. (b) Prove that n is an odd pseudoprime number if and only if 2"-1-1 mod n.
Number Representation and Calculation As you are going through the sections in Chapter 4, you will notice that we are working with different bases. Please explain to the class what it means to: Rewrite a number to a different base Add two or three numbers to a different base Subtract two numbers in a different base Why do we learn to work with numbers in different bases? Please provide examples of your answers. To begin the discussion, click on the...
Explain what a marginal means effect plot is and what it means to the analysis of the experiment.
Give the definition of what it means for a function, f(x)f(x), to be increasing on the interval ]a,b[]a,b[. Give the definition of what it means for a function, f(x)f(x), to be decreasing on the interval ]a,b[]a,b[. Note that your answer for (3) should be different from (2).
Let C, xxis a ternary (ie., base-3) number that is a multiple of n}. Show that for eachn> 1, the language C, is regular. Let C, xxis a ternary (ie., base-3) number that is a multiple of n}. Show that for eachn> 1, the language C, is regular.
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse and the contrapositive of the statement "If you earn an A in Math 52, then you understand modular arithmetic and you understand equivalence relations." Which of these d. Write the negation of the following statement in a way that changes the...
In the base conversion problem, the task to be performed is to convert the number of base n to decimal. The base of number can be anything such that all digits are represented using 0 to 9 and A to Z. Value of A is 10, Value for B is 11 and so on. So, write a program to convert a number to decimal Example: Input number is given as string and the output is an integer. Input Output Input...
2 (a) Consider two observables represented by operators A and B. Show that it is possible B if and only if A commutes with B to choose a complete set of eigenfunctions which are sharp in both A and For simplicity, you may assume that the eigenvalues of A are non-degenerate. [4] (b) how operators compatible with the Hamiltonian can be used to resolve the degeneracy Consider an example of a highly degenerate set of energy eigenfunctions. Explain [2] 2...