Thread: not understanding

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
where
p1p2... pn + 1
is not prime.

any help would be much appreciated

Originally Posted by pooshipple

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).

If then for some . Clearly then and since the conclusion follows.

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)

Sorry, I just noticed this. What it means to say that is that divides or that . Does that make a little more sense? So if then

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.

so then or and since the integers are closed under multiplication the conclusion follows.

31. Let a, b, and c be integers. Show that if a \ b and b \ c, then a \ c.

These all can be done the same. and . So then and the conclusion follows.

33. Give an example of consecutive primes p1 = 2, p2 ..., pn
where
p1p2... pn + 1
is not prime.

What does "consecutive" mean? That or that is merely the next prime in the list of primes? I'm assuming the latter. What do you think?