I have been reading/watching guides on reducing large numbers with exponents to smaller numbers to find the least nonnegative residue modulo. However, my simple mind cannot understand the process. One suggested dividing the initial exponent by 2. However, when I following the steps, I noticed that the base of the exponent changed to show congruency. I do not know what prompted him to change the base, leading to the reduction. Can anyone explain this process?
How to reduce numbers of exponent to find the least nonnegative residue modulo?
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elementary-number-theory
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0You need to reproduce his work here in some format, otherwise your question is classed as extremely broad. – 2017-02-01
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0http://math.stackexchange.com/questions/671859/find-the-least-nonnegative-residue I considered following the 2nd answer, where the person suggested dividing the exponent by 2 constantly. However, I could not find explanation or understand sufficiently to follow the procedure. – 2017-02-01
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0https://en.wikipedia.org/wiki/Exponentiation_by_squaring – 2017-02-01