Let a be an integer.(a) Explain why if a?kipi p... pr, then k; is even for each prime p1..:, r.(b) Show that if 5 divides a², then 5 divides a.(c) Hence show that 5 is irrational.

The detailed solution using basic properties of divisibility is presented in the next step.

Answered: Let a be an integer. ki k2 (a) Explain…

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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Let a be an integer. ki k2 (a) Explain why if a? 1,.. ki ... pir, then k; is even for each prime p, i ... ,r. (b) Show that if 5 divides a², then 5 divides a. (c) Hence show that 5 is irrational.