I was wondering why last digit of 5th power is the same as original number and the answer [1] is to look at x^5-x which is x(x²+1)(x+1)(x-1) and prove that it i

I was wondering why last digit of 5th power is the same as original number and the answer [1] is to look at x^5-x which is x(x²+1)(x+1)(x-1) and prove that it is divisible by 5 and 2 (by going through the possibilities) so it must be divisible by 10. Or [2] use euler theorem. There is a comment that (spoiler) the most general form is "The last digit of, any integer and its nth power, are the same, where n=4k+1." [1] https://answers.yahoo.com/question/index?qid=20071020225048AAfcZr6 https://answers.yahoo.com/question/index?qid=20071020225048A... [2] http://www.johndcook.com/blog/2015/07/04/when-the-last-digits-of-powers-dont-change/ http://www.johndcook.com/blog/2015/07/04/when-the-last-digit...