19 1900 ୬ ؠ 25 ୬ ሺmod 125ሻ ሺെ4ሻ ୬ ؠ 121 ୬ ሺmod 125ሻ
The whole expression: 121 ୬ െ 25 ୬ 25 ୬ െ 121 ୬ ؠ 0 ሺmod 125ሻ We can now reach the conclusion required that the expression is divisible by 2000 for every positive integer n.
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Division by 3
Add the number's digits. If the sum is evenly divisible by 3, then so is the number. So, will 3 divide evenly into 2,169,252? Yes it will, because the sum of the digits is 27, and 27 is divisible by 3. If you want, you can keep adding numbers until one digit remains. For example, keep going with 27. 2 + 7 = 9, which is also evenly divisible by 3.
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