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    NonNegative Residue-Modulo

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    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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    https://brainmass.com/math/number-theory/non-negative-residue-modulo-529392

    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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