Number Theory question QuestionGive a test for the divisibil

Number Theory question:

Question:Give a test for the divisibility of n by 2 depending on the digits of n when written to base 9.

Test for Divisibility of 2 in base 9

Just add all the ak\'s, if the sum of the number is even. then it is divisible by 2 otherwise it is not divisible by 2

Example

91(base 9) = 9 * 9 + 1 * 9^0 = 81 + 1 = 82 (82 is divisible by 2, (9+1) = 10 is divisible by 2), hence the test holds

85 (base 9) = 8 * 9 + 5 * 9^0 = 77, not divisible by 2, (8+5) = 13 also not divisible by 2

234(base 9) = 2 * 81 + 3 * 9 + 4 * 1 = 162 + 27 + 4 = 193, not divisble by 2, but (2+3+4), 9 is also not divisible by 2