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Grade 11Algebra

Using binomial theorem find the reminder when 5 raised to 103 is divided by 13

Profile image of Natarajan
10 Years agoGrade 11
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1 Answer

Profile image of Riddhish Bhalodia
ApprovedApproved Tutor Answer10 Years ago
5^{103} = 5.5^{102} = 5(26-1)^{51}
now expanding the above by binomial theorm all except for the constant term will be containing 26 which is divisible by 13
hence the remainder is
5(-1)^{51} = -5
which is the same as remainder being 8