(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

PROBLEM STATEMENT:

http://dpaste.com/0GN9MQ2

BOOK'S SOLUTION:

http://dpaste.com/0ZQ0YQM

2. Relevant equations

- m ⋅ u + n ⋅ v = 2ab
- GCD(a,b) ⋅ LCM(a,b) = ab
- z = 2 * LCM(a,b)
- z ?=? (m ⋅ u + n ⋅ v) / GCD(a,b)
3. The attempt at a solution

How does the author go from m ⋅ u + n ⋅ v = 2ab and GCD(a,b) ⋅ LCM(a,b) = ab to z = 2 * LCM(a,b)?

All I can think of is (m ⋅ u + n ⋅ v)/2 = GCD(a,b) ⋅ LCM(a,b) ⇒ (m ⋅ u + n ⋅ v) / GCD(a,b) = 2 ⋅ LCM(a,b). Is z = (m ⋅ u + n ⋅ v) / GCD(a,b)? If so, could someone please elaborate on the book's solution for that part? I don't see how one would go from it either being the case that z = u or that z = v (from the Pascal-style pseudo-code) to it being the case that z = (m ⋅ u + n ⋅ v) / GCD(a,b). Otherwise, if I'm completely off, could someone please just generally clarify how to solve this problem?

I would GREATLY appreciate it if someone could help me fully understand the solution to this problem!

P.S.

Also, what's the significance of all this? In other words, in addition to the solving of the problem itself, what's the big-picture takeaway from all this? Like, in simple terms, what was E. Dijkstra's motivation for doing this?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Given this modification to Euclid's algorithm, prove [...]

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**