hi rhymin

Sorry about the earlier muddle over the | symbol. This next bit is my excuse. Skip it if you like but it makes me feel better to have an excuse.

EXCUSE. It must be 45 years since I last saw that symbol in some number theory at Uni. What I should have done is looked it up rather than relying on a faulty memory. But I think the symbol is poorly chosen.

REASON. If we want to put "42 divided by 6" into symbols we can say 42 ÷ 6 or 42/6 or even

Now, division must have come long before the concept of "is it divible by" so someone must have made up that definition. Now he/she could have defined " divides " or " is divisible by ". The result is mathematically equivalent; it's all in the way you express the property. So why, oh why, did this person choose " divides " which puts the first number second and the second number first and just to be really confusing invent the symbol | for it, when | is already heavily used in maths to mean other things, and looks a lot like the symbol for divided by \ ???

No wonder I got mixed up.

END OF EXCUSE.

So, to make amends here is a method for creating the linear combination that doesn't require a computer.

We want integers s and t so that

Divide the larger number by the smaller ( 260/33)

Divide the larger number by the smaller (33/29)

Divide the larger number by the smaller (29/4)

When one of the 'coefficients' is 1 you can stop this process and jump to simultaneous equations.

Solving gives t = -25 and s = 197.

This pair are different from bobbym's pair but both sets of answers for s and t work. There are, in fact, an infinite number of solutions so best wishes to any teacher who has to check them all.

Bob