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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
theory Defs imports Main begin end
theory Submission imports Defs begin lemma modpower5: fixes n :: nat shows "n mod 10 = (n ^ 5) mod 10" sorry end
theory Check imports Submission begin lemma "(n::nat) mod 10 = (n ^ 5) mod 10" by (rule Submission.modpower5) end