Question

The unit's digit in the expansion of 2317^759

Answer 1

• 2317^759=(2310+7)^759

on binomial expansion, we find that the first teram is not divisible by 10 while others are divisible by 10.. SO only first term will contribute to last digit.. the first term is 7^759 the last digit of this will be the last digit of given question.' now observe the last digit in following arguments. 7^1=7, 7^2=49, 7^3=513 7^4=last digit being 1 and then the last digits repeat the last digits are 7,9,3,1,7,9,3,1, SO 7^(4n+1)---last digit is 7 7^(4n+2)---- last digit is 9 so on dividing 759 by 4 we get 3 as remainder... so the last digit will be 3 Digit in ones place=3