Given a number x=(x1x2x3...xn)10x = (x_1x_2x_3...x_n)_{10}x=(x1x2x3...xn)10 in decimal form, what is reminder divided by 3. Note that for any positive integer kkk, 10k≡1k≡1mod 3 10^k \equiv 1^k \equiv 1 \mod 3 10k≡1k≡1mod3Therefore, x=x110n−1+x210n−2+...+xn≡x1+x2+...+xnmod 3 x = x_1 10^{n - 1} + x_2 10^{n - 2} + ... + x^n \equiv x_1 + x_2 + ... + x_n \mod 3 x=x110n−1+x210n−2+...+xn≡x1+x2+...+xnmod3□\square□. ← Back to all notesBack to top ↑