Questions: 1. Prove or disprove each of the following statements. Note that you can use the fact that all prime numbers larger than 2 are odd. Also, for positive integers with at most 3 digits, you don't have to verify why they are/are not prime. For example, you can say that 271 is a prime, and 273 is not a prime without werifying. However, if you uso positive integers with more than 3 digits, you must verify why they are/are not primes. (a) There are integersxandylarger than 2 so thatxoryis a prime number, andx 2 +y 2 is a prime: (b) For all integersxandylarger than 2 , ifx 2 +y 2 is a prime thenxoryis a prime number. (c) There are integersxandylarger than 2 so thatxandyare prime numbers andx 2 +y 2 is a prime. (d) For all odd integersx, there are integersyandz50thatx 2 +y 2 =z 2 Questions:1. Prove or disprove each of the following statements. Note that you can use the fact that all prime numbers largerthan 2 are odd. Also, for positive integers with at most 3 digits, you don't have to verify why they are/are not prime. Forexample, you can say that 271 is a prime, and 273 is not a prime without verifying. However, if you use positive integerswith more than 3 digits, you must verify why they are/are not primes.(a) There are integers and y larger than 2 so that zor y is a prime number, and z² + y² is a prime.(b) For all integersz and y larger than 2, if rty is a prime then a or y is a prime number.(c) There are integersz and y larger than 2 so that z and y are prime numbers and a +y is a prime..(d) For all odd integers z, there are integers y and z so that x² + y²=2.

(a).Take x=5, y=4Then x is a prime number and Now So For all integers x, y such that x >2,…

Answered: Questions: 1. Prove or disprove each of…

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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Questions: 1. Prove or disprove each of the following statements. Note that you can use the fact that all prime numbers larger than 2 are odd. Also, for positive integers with at most 3 digits, you don't have to verify why they are/are not prime. For example, you can say that 271 is a prime, and 273 is not a prime without werifying. However, if you uso positive integers with more than 3 digits, you must verify why they are/are not primes. (a) There are integers x and y larger than 2 so that x or y is a prime number, and x 2 +y 2 is a prime: (b) For all integers x and y larger than 2 , if x 2 +y 2 is a prime then x or y is a prime number. (c) There are integers x and y larger than 2 so that x and y are prime numbers and x 2 +y 2 is a prime. (d) For all odd integers x , there are integers y and z50 that x 2 +y 2 =z 2