The digit sum of a nonnegative integer in a given base is the sum of its numerical digits. In base , replacing each power by shows that the integer and its digit sum are congruent modulo .

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The digit sum, also known as the sum of digits, is calculated by adding together all the individual digits of a given number. For instance, if you take the number 1234, the digit sum would be calculated as follows: 1 + 2 + 3 + 4 = 10 In this case, the digit sum of 1234 is 10. The concept is often used in various areas of mathematics, including number theory and numerical analysis.