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'Remainder Hunt' printed from https://nrich.maths.org/
What are the possible remainders when the $100^{th}$ power of an
integer is divided by $125$? To reduce the number of cases to be
checked, express the number as $5p+q $ where $p $ and $q $ are
integers and $q=1,2,3,4 $ and find the hundredth power using the
Binomial Theorem.