A client with hemоphiliа sustаins minоr fаcial trauma resulting in prоlonged bleeding. What would be the most appropriate immediate nursing intervention to manage this situation?
There аre 150 pоints pоssible оn this exаm. You need to show аll of your work and should only use methods shown in this course. Use the Euclidean Algorithm to [10] find all integer solutions (left(x,yright)) to [8925x+1836y=153] [5] write (frac{8925}{1836}) as a continued fraction. [10] Solve the following system of congruences. begin{align*}x&equiv 2pmod{3}\x&equiv 3pmod{7}\x&equiv 5pmod{11}end{align*} [10] Solve the following system of congruences:begin{align*}5x+3y&equiv 11pmod{14}\2x+y&equiv 9pmod{14}end{align*} [10] Find the value of the (infinite) continued fraction (left[0;overline{1,2}right]). Your answer should be in the form (a+bsqrt{d}), where (a,binmathbb{Q}) and (d) has no square factors. [10] Test the numbers (a=frac{245}{26}), (b=frac{113}{12}), and (c=frac{47}{5}), for whether they may be convergents for (2esqrt{3}). Show the work that validates your conclusions, which in each case should be yes, no, or maybe. [10] Show how to reduce the residue (171^{139}pmod{240}) Let (N=23814=2cdot 3^{5}cdot 7^{2}). Find each of the following values. [5] (sigmaleft(Nright)) [5] (tauleft(Nright)) [10] Suppose that (Fleft(nright)=displaystyle{sum_{dmid n}}fleft(dright)), and that the first (20) values of (F) are as in the following table. Show how to find (fleft(20right)).(begin{array}{|c|c|c|c|c|}hlinen&Fleft(nright)&&n&Fleft(nright)\hlinehline1&1&&11&21\hline2&4&&12&66\hline3&6&&13&32\hline4&11&&14&48\hline5&5&&15&30\hline6&24&&16&74\hline7&12&&17&40\hline8&23&&18&80\hline9&20&&19&46\hline10&20&&20&55\hlineend{array}) [10] Use the following table to factor (48361) via Kraitchik's method. Hint: Find two additional lines that will work with (a=221) (for a total of three lines used).(begin{array}{|c|c|c|}hlineN&N^{2}-48361&text{factorization}\hlinehline220&39&3times 13\hline221&480&2^{5}times 3times 5\hline222&923&13times 71\hline223&1368&2^{3}times 3^{2}times 19\hline224&1815&3times 5times 11^{2}\hline225&2264&2^{3}times 283\hline226&2715&3times 5times 181\hline227&3168&2^{5}times 3^{2}times 11\hline228&3623&3623\hline229&4080&2^{4}times 3times 5times 17\hline230&4539&3times 17times 89\hline231&5000&2^{3}times 5^{4}\hline232&5463&3^{2}times 607\hlineend{array}) Primitive Roots modulo 41. Use the table at the end of the exam to answer these questions. [5] Using the table, what are the values of (text{ind}_{7}left(15right)) and (text{ord}left(18right)). [10] Use the table to find all incongruent solutions to (16x^{24}equiv 18pmod{41}). [10] Use Legendre symbols to determine whether the congruence (x^{2}equiv 149pmod{253}) has any solutions. (Note: (149) and (253) are primes.) [10] (x=13) is a solution to (x^{2}equiv 5pmod{41}). Lift this to a solution to (x^{2}equiv 5pmod{41^{2}}). You are a user of the RSA Public Key Cryptography program. Your two primes are (p=283) and (q=661). [5] Assume your public key (not modulus, (n), which is (pq)) is (e=637). What congruence would you have to solve to find your secret key, (d)? [5] Describe briefly how (e) and (d) are used by the sender and/or recipients, assuming that the sender wants to encrypt and send a message block (m). You are a user of a Knapsack Cryptography system. Your private sequence is [1,3,5,11,24,48,97,192] Your modulus, which is also private, is (m=200). Your multiplying factor, (a), is chosen to be (117), with corresponding decoding factor (c=53). [5] Show how to get your public sequence. [5] Someone sends you a message where one of the (encrypted) blocks is the number (588). Which binary string does this block correspond to? Your answer should be a length-8 bit string, eg (10101010). (begin{array}{|c|c|c|c|c|c|c|c|}hlinek&7^{k}pmod{41}&k&7^{k}pmod{41}&k&7^{k}pmod{41}&k&7^{k}pmod{41}\hlinehline1&7&11&22&21&34&31&19\hline2&8&12&31&22&33&32&10\hline3&15&13&12&23&26&33&29\hline4&23&14&2&24&18&34&39\hline5&38&15&14&25&3&35&27\hline6&20&16&16&26&21&36&25\hline7&17&17&30&27&24&37&11\hline8&37&18&5&28&4&38&36\hline9&13&19&35&29&28&39&6\hline10&9&20&40&30&32&40&1\hlineend{array})