What is the last digit of N ?

What is the last digit of N, where N = (21)^101 + (17)^116 + (29)^29

1 Answer
May 4, 2018

The rightmost digit is 1.

Explanation:

Working (mod 10)

21^{101} + 17^{116} + 29^29

equiv 1^{101} + 7^{116} + (-1)^29

equiv 1 + 7^{116} + -1

equiv (7^4)^{29}

equiv (49^2)^{29}

equiv ((-1)^2)^{29}

equiv 1

so the rightmost digit is 1.