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8. Keep the notation from Podasip 7. If p is an odd prime and a ‡ 0(mod p), then... p-1 (a)…a²¹ = (−1)ª(mod p) where N is the number of € that are negative. + €(p-1)/2· p-1 (b)...a²2 = (−1)M (mod p) where M = €1 + €2 + 2

8. Keep the notation from Podasip 7. If p is an odd prime and a ‡ 0(mod p), then... p-1 (a)…a²¹ = (−1)ª(mod p) where N is the number of € that are negative. + €(p-1)/2· p-1 (b)...a²2 = (−1)M (mod p) where M = €1 + €2 + 2

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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Podasip p-1 7. Suppose p is an odd prime and a ‡ 0(mod p). For each k = 1, 2,…, pz¹ define Ek and rk by 2 ak Ekrk (mod p) where 0<rk </ and Ek 2 +1 Then those remainders r1, 72, ..., (p-1)/2 are distinct. r 8. Keep the notation from Podasip 7. If p is an odd prime and a ‡ 0(mod p), then... p-1 (a).. α 2 = (−1)ª (mod p) where N is the number of € that are negative. (b)... a² = (-1) M (mod p) where M = €₁ + €2 + · ·· + €(p−1)/2. p-1 =
Transcribed Image Text:Podasip p-1 7. Suppose p is an odd prime and a ‡ 0(mod p). For each k = 1, 2,…, pz¹ define Ek and rk by 2 ak Ekrk (mod p) where 0<rk </ and Ek 2 +1 Then those remainders r1, 72, ..., (p-1)/2 are distinct. r 8. Keep the notation from Podasip 7. If p is an odd prime and a ‡ 0(mod p), then... p-1 (a).. α 2 = (−1)ª (mod p) where N is the number of € that are negative. (b)... a² = (-1) M (mod p) where M = €₁ + €2 + · ·· + €(p−1)/2. p-1 =
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