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?

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- November 20th 2009, 11:51 AMsteph3824Find 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?

- November 20th 2009, 12:06 PMgmatt
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.

- November 20th 2009, 01:24 PMmosta86
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 .