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Number theory in high school mathematics competition
What do you want to ask? The first one is because the integer part can be expressed like this.

Because if a+b is a positive integer and b is greater than 0 and less than 1, then the last digit of a+b is the single digit of a plus 1.

The circle behind indicates that the remainder according to module 5 is a periodic function (period is 3). 20 13 can be divisible by 3, and the first, second and third remainders are 4, 4 and 2 respectively, so dividing 20 13 by 5 should be the remainder 2 (the same as the third term).

Because the sequence is even, the unit number of item 20 13 is 2, so the unit number is 1.