question

Prove that every integer is congruent mod 9 to the sum of its digits.

Thank you very much.

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- January 11th 2007, 11:36 AMJenny20congruent mod 9
question

Prove that every integer is congruent mod 9 to the sum of its digits.

Thank you very much. - January 11th 2007, 12:22 PMThePerfectHacker
- January 11th 2007, 08:07 PMSoroban
Hello, Jenny!

Here's a more "primitive" proof . . .

Quote:

Prove that every integer is congruent mod 9 to the sum of its digits.

We have an integer of the form:

Its value is: .

The sum of its digits is: .

Consider their difference:

. .

All the coefficients are of the form:

. . and hence are divisible by 9.

Since is a multiple of 9: .