Question $1$: $[15$ points$]($a$)[2$ points$]$ Discuss why $100.\mathrm{.}0|\{$z $\}$m $1($mod $9)$ for every m $2($b$)[3$ points$]$ Prove that the remainder of any number modulo $9$ isequal to the remainder of the sum of its digits modulo $9.$ As anexample$152311+5+2+3+1123($mod $9)($You can also try to come up with a method to find the remainderof a number modulo $11$ using similar type of ideas. No need to writeit down, but try to solve it ;) $)($c$)[10$ points$]$ Imagine we write the numbers $1,2,,2024$ from leftto right to create the following numberx $=1234567891011121320232024$What is the remainder of this number modulo $9.$Hint: You might try to add the digits but this will be really hardand is not a good idea here. Because then you have to calculate howmany times each digit appears which is not easy. You might wantto use similar type of ideas, but smarter $=)$