Suppose you need to work with and store the integer M-5857458478 on some device with very...

 

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Suppose you need to work with and store the integer M-5857458478 on some device with very limited power; the device cannot store any numbers larger than 100 or do any calculations with numbers larger than 100. But you need to do some basic arithmetic calculations with M on that device. You could store each digit of M in ten individual files and identify which file corresponds to which digit but then arithmetic calculations with M may be intricate: you want to find an easier approach. (i) Note that 2-3-5-7-11-13-17-19-23-29=6469693230 > M and use the Chinese Remainder Theorem to design an intelligent means to store M that will enable basic calculations with the ten digit number M. Be sure to explicitly state how M is stored. (ii) Use your design from (i) to calculate and store the outcome of the M-4927100893 on the device and explain how you arrived at your answer.. (iii) First, use your design from (i) to represent 44777 on the device and then use that representation to calculate the representation of the inverse of 44777 (mod M) and, then, finally, use that answer to represent the value of M/44777. (You should not be performing any division by 44777; you can only use operations the device can support as described in the question). Suppose you need to work with and store the integer M-5857458478 on some device with very limited power; the device cannot store any numbers larger than 100 or do any calculations with numbers larger than 100. But you need to do some basic arithmetic calculations with M on that device. You could store each digit of M in ten individual files and identify which file corresponds to which digit but then arithmetic calculations with M may be intricate: you want to find an easier approach. (i) Note that 2-3-5-7-11-13-17-19-23-29=6469693230 > M and use the Chinese Remainder Theorem to design an intelligent means to store M that will enable basic calculations with the ten digit number M. Be sure to explicitly state how M is stored. (ii) Use your design from (i) to calculate and store the outcome of the M-4927100893 on the device and explain how you arrived at your answer.. (iii) First, use your design from (i) to represent 44777 on the device and then use that representation to calculate the representation of the inverse of 44777 (mod M) and, then, finally, use that answer to represent the value of M/44777. (You should not be performing any division by 44777; you can only use operations the device can support as described in the question).

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i To store the integer M 5857458478 using the Chinese Remainder Theorem we need to find a set of remainders that are relatively prime to each other an... View the full answer