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Determine whether each of the following congruences is solvable, and find the number of incongruent solutions of the each congruence. (i) x² = -471 mod 4. 136. 238.4131 (ii) x² = -471 mod 28. 2312.61¹1 (iii) x² = -471 mod 3.4115 (iv) x² = -471 mod 35 - 23²

Determine whether each of the following congruences is solvable, and find the number of incongruent solutions of the each congruence. (i) x² = -471 mod 4. 136. 238.4131 (ii) x² = -471 mod 28. 2312.61¹1 (iii) x² = -471 mod 3.4115 (iv) x² = -471 mod 35 - 23²

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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(4) Determine whether each of the following congruences is solvable, and find the number of incongruent solutions of the each congruence. (i) x² = -471 mod 4 · 136 . 238.4131 (ii) x² = −471 mod 28. 23¹2.6111 (Hint: See Theorem 10.12 in our Lecture Notes.) (iii) x² = −471 mod 3.41¹5 (iv) x² = −471 mod 35.232
Transcribed Image Text:(4) Determine whether each of the following congruences is solvable, and find the number of incongruent solutions of the each congruence. (i) x² = -471 mod 4 · 136 . 238.4131 (ii) x² = −471 mod 28. 23¹2.6111 (Hint: See Theorem 10.12 in our Lecture Notes.) (iii) x² = −471 mod 3.41¹5 (iv) x² = −471 mod 35.232
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