Cookies disclaimer

I agree Our site saves small pieces of text information (cookies) on your device in order to deliver better content and for statistical purposes. You can disable the usage of cookies by changing the settings of your browser. By browsing our website without changing the browser settings you grant us permission to store that information on your device.

[2018-Oct] Fun modulo 5

Could you believe it? Stefan just was playing around with his favorite numbers, he wanted to practice taking the fifth power of them, when suddenly he realized, that the least significant digit of the result was the same as the original number's. Can you show him why?

That is, prove: n mod 10 = (n ^ 5) mod 10

Resources

Download Files

Definitions File

theory Defs
  imports Main
begin
end

Template File

theory Submission
  imports Defs
begin

lemma modpower5: fixes n :: nat
  shows "n mod 10 = (n ^ 5) mod 10" sorry


end

Check File

theory Check
imports Submission
begin
                     
lemma "(n::nat) mod 10 = (n ^ 5) mod 10"
by (rule Submission.modpower5)

end

Terms and Conditions