Question 1Make sure that all your answers are explained carefully.(a) Find the prime factorisation of 75, 460.(b) Find the greatest common divisor of a =(c) Find the largest integer k such that 7k divides 567!.(d) How many of the 100 numbers 213! +2, 213! +3,..., 213! + 101 are composite?(e) Find all solutions of the following Diophantine equation or prove that there are no integralsolutions: 45x - 215y = 24.22022 and b = 7590236870340321.

We will use simple factorization process to solve these problems.

Answered: Make sure that all your answers are…

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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Make sure that all your answers are explained carefully. (a) Find the prime factorisation of 75, 460. (b) Find the greatest common divisor of a = 22022 and b = 7590236870340321. (c) Find the largest integer k such that 7k divides 567!.