Ex 5: Led F be a field and let Pr). Jcx) E fcx]. IF there exisls no polynomi als ol +ve degree in Fex) that divide o 8 1x) , • prove that there exuats hex),kız) E F[x] such that fiox) hea) (In this case , f8 are naid do be re latively pime) Jn kex)-1
Ex 5: Led F be a field and let Pr). Jcx) E fcx]. IF there exisls no polynomi als ol +ve degree in Fex) that divide o 8 1x) , • prove that there exuats hex),kız) E F[x] such that fiox) hea) (In this case , f8 are naid do be re latively pime) Jn kex)-1
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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![Ex 5: Let F be a field and let Po). Jcx) E fcx] .
IF there exisls no
polynomials o +ve degiee sn Fex) that divide
fix) + J 1x)
• prove that there exiâts hex),k(x) E F[x] such that
fox) hea) + dxm kex)= 1
(In this case , f B8 are said to be re latively pime)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ab93f9c-673c-430e-8f40-b9ff2fdb64ad%2F64fc7498-ff1d-45d7-ad25-b08123c61e89%2Fy6zb42_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Ex 5: Let F be a field and let Po). Jcx) E fcx] .
IF there exisls no
polynomials o +ve degiee sn Fex) that divide
fix) + J 1x)
• prove that there exiâts hex),k(x) E F[x] such that
fox) hea) + dxm kex)= 1
(In this case , f B8 are said to be re latively pime)
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