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

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

Grade:11

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 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

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