1. Without a calculator or a computer, and with clear explanation using the criterion developed in class, determine if the number N= 850300572 is divisible by 11. (Answer without explanation receives no credit) 2. Using the technique learned in class, develop as best as you can a criterion of divisibility by 7. State your final answer clearly. 3. Prove: for every integer n and for every odd integer a, a" = 1 (mod 2n+2) 4. Let m>0, then a complete system of remainders modulo m (CSR) is a set of m integers, 71, 72,..., Tm no two of which is congruent modulo m.Example: 0, 1, 2, 3, ...., m - 1 (This is just an example) Without a calculator or a computer, and clearly showing the steps, explain why the set (1, 3, 32, 3,..., 315} constitutes a CSR modulo 17 (Make sure you read the definition of a CSR carefully, then proceed)