For each part, use the data provided to find values of a and b satisfying a2 ≡ b2 (mod N), and then compute gcd(N, a − b) in order to find a nontrivial factor of N. (c) N = 198103 11892 ≡ 27000 (mod 198103) and 27000 = 23 · 33 · 53 16052 ≡ 686 (mod 198103) and 686 = 2 · 73 23782 ≡ 108000 (mod 198103) and 108000 = 25 · 33 · 53 28152 ≡ 105 (mod 198103) and 105 = 3 · 5 · 7

For each part, use the data provided to find values of a and b satisfying a2 ≡ b2 (mod N), and then compute gcd(N, a − b) in order to find a nontrivial factor of N. (c) N = 198103 11892 ≡ 27000 (mod 198103) and 27000 = 23 · 33 · 53 16052 ≡ 686 (mod 198103) and 686 = 2 · 73 23782 ≡ 108000 (mod 198103) and 108000 = 25 · 33 · 53 28152 ≡ 105 (mod 198103) and 105 = 3 · 5 · 7

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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Question

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For each part, use the data provided to find values of a and b satisfying a² ≡ b² (mod N), and then compute gcd(N, a − b) in order to find a nontrivial factor of N.

1189² ≡ 27000 (mod 198103) and 27000 = 2³ · 3³ · 5³

1605² ≡ 686 (mod 198103) and 686 = 2 · 7³

2378² ≡ 108000 (mod 198103) and 108000 = 2⁵ · 3³ · 5³

2815² ≡ 105 (mod 198103) and 105 = 3 · 5 · 7

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