# Residue Systems : Modulo

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5. If m = 11, then a reduced residue system modulo m is 1,2,3,4,5,6,7,8,9,10. Exhibit the pairing of each of the preceding numbers with its inverse modulo m (like Chinese remainder theorem).

7. What is the remainder when 41^5 is divided by 3? When 473^38 is divided by 5?

8. Prove that if p is a prime congruent to 1 modulo 4, then ... (see attachment for details).

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#### Solution Summary

Residue systems are investigated in the solution.

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