RINGS

Do the assingment

diophantine equation

State and prove Chinese remainder theorem The linear congruence 𝑎𝑥 ≡ 𝑏(𝑚𝑜𝑑𝑚) is solvable if and only if 𝑑/𝑏, where 𝑑 = (𝑎, 𝑚). If 𝑑/𝑏, then it has d incongruent solutions (i) Prove that an integer is divisible by 3 if the sum of its digits id divisible by 3. (ii) Prove that an integer is divisible by 9 if the sum of its digits id divisible by 9.