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1. Use the approach of the Great Theorem of Chapter 10 to determine if 1,679,617 is prime just as Euler did for 232 +1. (a) First find some even number a and the largest value of n such that 1,679, 617 = a" + 1. (b) Based on the above and Euler's Theorems what form must a prime divisor of 1,679,617 have? (c) Calculate the maximum number of possible divisors of 1,679,617 that it may be necessary to check.

1. Use the approach of the Great Theorem of Chapter 10 to determine if 1,679,617 is prime just as Euler did for 232 +1. (a) First find some even number a and the largest value of n such that 1,679, 617 = a" + 1. (b) Based on the above and Euler's Theorems what form must a prime divisor of 1,679,617 have? (c) Calculate the maximum number of possible divisors of 1,679,617 that it may be necessary to check.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Use the approach of the Great Theorem of Chapter 10 to determine if 1,679,617 is prime just as Euler did for 232 +1. (a) First find some even number a and the largest value of n such that 1, 679, 617 = a²" + 1. (b) Based on the above and Euler's Theorems what form must a prime divisor of 1,679,617 have? (c) Calculate the maximum number of possible divisors of 1,679,617 that it may be necessary to check. (d) Complete the following table for each of the possible divisors that you try. k p= (2"+1) k +1 Comment (e) Were you as lucky as Euler was? Explain.
Transcribed Image Text:1. Use the approach of the Great Theorem of Chapter 10 to determine if 1,679,617 is prime just as Euler did for 232 +1. (a) First find some even number a and the largest value of n such that 1, 679, 617 = a²" + 1. (b) Based on the above and Euler's Theorems what form must a prime divisor of 1,679,617 have? (c) Calculate the maximum number of possible divisors of 1,679,617 that it may be necessary to check. (d) Complete the following table for each of the possible divisors that you try. k p= (2"+1) k +1 Comment (e) Were you as lucky as Euler was? Explain.
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