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# NonNegative Residue-Modulo

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16. Find the least non-negative residue of:
(i) 5^18 mod 11;
(ii) 4^47mod 12;

28. Show that 11 divides 10a+b if and only if 11 divide a - b. Use this to show that 11 divides 232595.

30. Find the lease non-negative residues mod 7, 11 and 13 of 58473625.

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#### Solution Preview

** Please see the attachment for the complete solution **
16. We wish to find the following least nonnegative residues:
(please see the attached file)
(i)
(please see the attached file)

We have:
(please see the attached file)

where we used the fact that (please see the attached file), due to Fermat's little ...

#### Solution Summary

In this solution we solve several problems in modular arithmetic.

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