Turn on thread page Beta
    • Thread Starter

    Let a, b, c, d be strictly positive integers. Prove the following:
    (a) If a|b and b|c and gcd(a, c) = 1, then we must have a = 1.
    (b) If a|c, b|c and gcd(a, b) = d, then ab|cd.
    [Hint: Bézout is helpful.]
    (c) If gcd(a, c) = 1 and gcd(b, c) = d, then gcd(ab, c) = d.
    [Hint: what can you say about numbers which divide both ab and c
Submit reply
Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Updated: November 7, 2017


students online now


Exam discussions

Find your exam discussion here

Should universities take a stronger line on drugs?

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.