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a) i. Let M and 4 be any two numbers of the form 42+1 ii. Let Mand N be any off the form 4r +3 Prove that in both coses (i) and (ii) the product M. N is the form 47+1 two numbers 익

a) i. Let M and 4 be any two numbers of the form 42+1 ii. Let Mand N be any off the form 4r +3 Prove that in both coses (i) and (ii) the product M. N is the form 47+1 two numbers 익

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a) i. Let M and 4 be any two numbers N the form 4r+1 of ii. Let M7 and N be any two numbers the form 4r +3 of Prove that in both cases (i) and (ii) the 7. 시 is 익 the form 47+1 product 6) Now Suppose that {P₁, P₂, P3, ..., P₁3 is a finite collection of primes of the form 47 +3 Me introduce the number - N = 4( P ₁ • P ₂ ⋅ P3 • ... · Pk) - 1. Mimic the proof of Guclid's ( for Infinitude of Primes to show that there are infinitely many primes of the form 4r +3. how Make sure to clearly indicate where and you are using port (a) in the proof of part (6) !
Transcribed Image Text:a) i. Let M and 4 be any two numbers N the form 4r+1 of ii. Let M7 and N be any two numbers the form 4r +3 of Prove that in both cases (i) and (ii) the 7. 시 is 익 the form 47+1 product 6) Now Suppose that {P₁, P₂, P3, ..., P₁3 is a finite collection of primes of the form 47 +3 Me introduce the number - N = 4( P ₁ • P ₂ ⋅ P3 • ... · Pk) - 1. Mimic the proof of Guclid's ( for Infinitude of Primes to show that there are infinitely many primes of the form 4r +3. how Make sure to clearly indicate where and you are using port (a) in the proof of part (6) !
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