Can you solve this discrite math and computer science questions? with solutions and explainitions .

Prove or disprove: For all integers a, b, c, d, if a\b and c\d, then (ac)\(b + d). Prove or disprove: For all integers a, b, c, if a\bc, then a\b or a\c. Find the prime factorization of 45617. List all positive integers less than 30 that are relatively prime to 20. Prove or disprove: The sum of two primes is a prime. Prove or disprove: If p and q are primes (both > 2), then pq + 1 is never prime. Find the smallest integer a > 1 such that a + 1 = 2a (mod 11). Use the Euclidean Algorithm to find gcd(900,140). Show all intermediate results. You are encouraged to write short programs to solve some of the above problems; there is no need to submit your code