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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.
Remainder Hunt
Age 16 to 18
Challenge Level 
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.
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