How much is the remainder of 3 divided by 13 to the power of 2000

3^2000=3^1998*3^2=3^1998*9
3^1998=3^(3*666)=27^666=(2*13+1)^666,mod(3^1998,13)=1
mod(3^2000,13)=mod(3^1998*9,13)=mod(3*1998,13)*9=9

What is the remainder of 1995 × 1996 × 1997 × 1998 × 1995 divided by 13?

1995 = 13 * 153 + 6, the same as 1996 = 13 * 153 + 7, 1998 = 13 * 153 + 8, substituting into the original problem, we need to make clear a theorem that is the multiple of 13 multiplied by any integer or the multiple of 13, so we will only consider the multiplication result of items without 13 multiple, then 6 * 7 * 8 * 6 = 2016, divide by 13 to get 155 odd 1, then the remainder is 1

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