What is the last digit of N ?

Question

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

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Answer 1 · 2018-05-04T11:10:39

The rightmost digit is 1.

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.