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Problem 6 . Let p be a prime of the form 4k+ 1 such that p = m² +n², where m and n are integers and m is odd. (a) Suppose q is an arbitrary prime factor of m. Find the Legendre symbol (2). to find the Legendre symbol (² ? (m+n)² - 1 8 n (b) Show that · (m + ¹) = (-1) ² P Use this

Problem 6 . Let p be a prime of the form 4k+ 1 such that p = m² +n², where m and n are integers and m is odd. (a) Suppose q is an arbitrary prime factor of m. Find the Legendre symbol (2). to find the Legendre symbol (² ? (m+n)² - 1 8 n (b) Show that · (m + ¹) = (-1) ² P Use this

Advanced Engineering Mathematics
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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Problem 6 . Let p be a prime of the form 4k+ 1 such that p = m² + n², where m and n are integers and m is odd. (a) Suppose q is an arbitrary prime factor of m. Find the Legendre symbol (2). to find the Legendre symbol (² ? (b) Show that (m+n) = (-1) (m + n)² - 1 8 Use this
Transcribed Image Text:Problem 6 . Let p be a prime of the form 4k+ 1 such that p = m² + n², where m and n are integers and m is odd. (a) Suppose q is an arbitrary prime factor of m. Find the Legendre symbol (2). to find the Legendre symbol (² ? (b) Show that (m+n) = (-1) (m + n)² - 1 8 Use this
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