# NonNegative Residue-Modulo

Could you please help explain these problems?:

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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