How does addition and subtraction effect factors

[sumithshah]

Hi

I have a question - lets say two integers M and N leave remainders P and Q when divided by R and S, how would I find a common factor for M-N

So basically the question boils down to how does addition / subtraction effect factors / is there a rule you guys can point me to?

[Guest]

This is the rule:

If 2 numbers have a common divisor then their sums and differences also have the common divisor

Eg:

6 has 2 as a divisor
10 has 2 as a divisor

Then 6+10 = 16 also has 2 as a divisor
10-6 = 4 also has 2 as the divisor

[esledge]

More generally:

(multiple of x) +/- (multiple of x) = multiple of x
(non-multiple of x) +/- (multiple of x) = non-multiple of x
(non-multiple of x) +/- (non-multiple of x) = EITHER multiple of x OR non-multiple of x (i.e. it depends on whether the remainders sum to x.)

Watch out--this gets trickier when remainders are specified, as you can't assume that the remainder of the sum or difference is simply the sum or difference of the original remainders.

For example: 8 has remainder 3 when divided by 5. 9 has remainder 4 when divided by 5. The sum 8 + 9 = 17 has remainder 2 when divided by 5. In other words, the remainder of the sum is (3 + 4) - 5 = 7 - 5 = 2.

[hassan]

Hi ,

The information provided from above posts is quite intutive but would some 1 care to quote a Question where we would see the practical application of this concept or atleast quote the source where we could get Qs on this Concept.

SIde note : (Quoting Qs of the aforementioned concept would be more helpful )

Regards

[JonathanSchneider]

Great question, Hassan. I don't know of any problems off the top of my head that are exactly like this one. There are, however, a number of great remainder problems in the OG. I'd start with D13, in the Diagnostic test.