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# if p|q and p|r, when q>r then ?

### 2 Answers

- Iggy RockoLv 72 months ago
p|q so q = pa for some a.

p|r so r = pb for some b.

Create a counterexample to show the dark blue choice is false.

Let p = 2, r = 4, and q = 6.

2|6 and 2|4, but r|q = 4|6 is false.

For the light blue choice,

q - r =

pa - pb =

p(a - b)

Since a and b are integers, p|(q - r).

For the yellow choice

qr = papb = p(apb). Since a, b, and p are integers, p|qr.

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- PopeLv 72 months ago
These are all positive integers, right?

p | q → q = pa, for some positive integer a

p | r → r = pb, for some positive integer b

q > r

pa > pb

a > b

a - b > 0

That makes (a - b) a positive integer.

q - r = pa - pb

q - r = p(a - b)

p | (q - r)

qr = par

p | (qr)

q = pa

q = pb(a/b)

q = r(a/b)

Therefore, r | q only if b | a.

It cannot be concluded that r | q.

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- PopeLv 72 months agoReport
You mean which two are correct. Those would be the two I gave you.

p | (q - r)

p | (qr) - Login to reply the answers