5.4.4 In this question we use recall an alternative definition of prime.19Definition. p E N>2 is prime if Va, b E N, p|ab = p|a or p|b.→ pla or p|b.Let p be prime, let n E N, and let a1,...,an be natural numbers such that p divides the productajd2 · · · An. Prove by induction that,3i e {1,2,...,n} such that p|a;.Hint:need to cover two base cases.Why? Think about the induction step first and it will help youyoudecide howтаnybase cases youneed.

Given definition is, p∈ℕ≥2 is prime if ∀a,b∈ℕ, p|ab ⇒ p|a or p|b. Also given that p be a prime, and…

5.4.4 In this question we use recall an alternative definition of prime.19 Definition. p E N>2 is prime if Va, b E N, p|ab = p|a or p|b. Let p be prime, let n e N, and let a1,...,an be natural numbers such that p divides the product aja2·.. an. Prove by induction that, 3i e {1,2,...,n} such that p|a;.

5.4.4 In this question we use recall an alternative definition of prime.19 Definition. p E N>2 is prime if Va, b E N, p|ab = p|a or p|b. Let p be prime, let n e N, and let a1,...,an be natural numbers such that p divides the product aja2·.. an. Prove by induction that, 3i e {1,2,...,n} such that p|a;.

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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