0 like 0 dislike
0 like 0 dislike
Need help on understanding divisibility proof

1 Answer

0 like 0 dislike
0 like 0 dislike
If a and b are both divisible by d, then a and b are *multiples* of d. Then there are two integers, k and L, such that dk = a and dL = b.

Step 1: Here, they are just substituting dk for a and dL for b.
> ax + by = (dk)x + (dL)y

Step 2: Looking at the right hand side of the equation above, factor out the d.
> dkx + dLy = d(kx + Ly)

> So ax + by = d(kx + Ly)

Step 3: Since multiplying two integers together gives you an integer, kx and Ly must both be integers. And since adding two integers together gives you an integer, we also know that kx + Ly is an integer as well. This means that d(kx + Ly) is an integer that is obviously divisible by d.

Here, they say this by introducing a new integer called k’ such that k’ = kx + Ly.
> d(kx + Ly) = dk’

> So ax + by = dk’ which means that ax + by is also divisible by d.

No related questions found

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!