Find the order of the element (2, 3) in the direct product group Z4 × 28. Compute the exponent and the order of the group Z₁0 × Z12. LLY

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Answer 20 and 21
20. Find the order of the element (2, 3) in the direct product group Z4 × 28.
21. Compute the exponent and the order of the group Z10 x Z12.
22. Let d = ged(a, b). Prove that ged(a/d, b/d) = 1.
23. Find the unique solution in Z4300 of the system of congruences
Transcribed Image Text:20. Find the order of the element (2, 3) in the direct product group Z4 × 28. 21. Compute the exponent and the order of the group Z10 x Z12. 22. Let d = ged(a, b). Prove that ged(a/d, b/d) = 1. 23. Find the unique solution in Z4300 of the system of congruences
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