Thread: Find the last digit

Find the last digit of 541^(341). Clearly, the last digit would be one, but I don't know how to go about showing that it would be one. Can someone help please?

i.e. the last digit is going to be 1. If this doesn't make sense to you prove it by induction. I.e. prove that has ending digit one for all n.

by induction : 541^n ,
for n = 1 , 541^1 = 541 => it ends with 1 true
assume that 541^k ends with one is true and proof that 541^(k+1) ends with one
now 541^(k+1) = 541^k * 541 ,,, we prooved that 541^k ends with one and 541 ends with one the multiplication of two numbers that ends with one will result in a number that ends with one .