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2. Find the Eurler's function of 45, i.e., (45) =? 3. For n EN and p is prime, prove that (nlp - 1 and p|n3 - 1) (4p- 3 is a perfect square) 4. Find gcd(x + 1,x² + 1) and then solve x3 + x2 + x + 1= y² 5. Use Euler's Theorem to compute 2905 mod 341, where 341-11.31 6. Wilson's theorem states that if p is prime, then (p - 1)! = -1 mod p, calculate %3D (р - 2)! тоd p 7. Solve in Z: 1+ 8x2 = y2

2. Find the Eurler's function of 45, i.e., (45) =? 3. For n EN and p is prime, prove that (nlp - 1 and p|n3 - 1) (4p- 3 is a perfect square) 4. Find gcd(x + 1,x² + 1) and then solve x3 + x2 + x + 1= y² 5. Use Euler's Theorem to compute 2905 mod 341, where 341-11.31 6. Wilson's theorem states that if p is prime, then (p - 1)! = -1 mod p, calculate %3D (р - 2)! тоd p 7. Solve in Z: 1+ 8x2 = y2

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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2. Find the Eurler's function of 45, i.e., $(45) =? 3. For n E N and p is prime, prove that (n|p – 1 and p|n³ – 1) → (4p- 3 is a perfect square) 4. Find gcd(x+ 1,x² + 1) and then solve x³ + x² + x + 1 = y? 5. Use Euler's Theorem to compute 2905 mod 341, where 341=11.31 6. Wilson's theorem states that if p is prime, then (p – 1)! = -1 mod p, calculate %3D (р - 2)! тоdp 7. Solve in Z:1+ 8x² = y² %3D
Transcribed Image Text:2. Find the Eurler's function of 45, i.e., $(45) =? 3. For n E N and p is prime, prove that (n|p – 1 and p|n³ – 1) → (4p- 3 is a perfect square) 4. Find gcd(x+ 1,x² + 1) and then solve x³ + x² + x + 1 = y? 5. Use Euler's Theorem to compute 2905 mod 341, where 341=11.31 6. Wilson's theorem states that if p is prime, then (p – 1)! = -1 mod p, calculate %3D (р - 2)! тоdp 7. Solve in Z:1+ 8x² = y² %3D
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