have to do a couple problems for homework and im not understanding exactly what is going on and why its the answer
27. Let m, n, and d be integers. Show that if d \ m and d \ n, then d\ (m - n).
my professor gave us the answer to this but i do not understand why it works
answer: m = dq1 n = dq2 m - n = dq1 - dq2 = d(q1 - q2) therefore d \ (m - n)
these are the other problems i have to do
28. Let m, n, and d be integers. Show that if d \ m, then d \ mn.
31. Let a, b, and c be integers. Show that if a \ b and b \ c, then a \ c.
33. Give an example of consecutive primes p1 = 2, p2 ..., pn
p1p2... pn + 1
is not prime.
any help would be much appreciated