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 &quot;The last digit of, any integer and its nth power, are the same, where n=4k+1.&quot;<p>[1] 
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