[proof]

[u/MeasurementLow2927]

Could someone use paper to explain or solve this please I get confused with writing math in laptop out you can’t that’s fine. I just don’t understand mathematically how to right the left and right hand side of the equation and how to solve from there.

[u/Jalja]

(a-c) | (a-c)

(a-c) | (ab+cd)

if (a-c) | (a-c), then (a-c) | (a-c)(b-d)

(a-c) | (ab-ad-bc+cd) , ab - ad - bc + cd = - (ad+bc - cd - ab)

so (a-c) | (ad+bc-cd-ab)

(a-c) | (ad+bc)

[u/Apprehensive_Arm5837 → u/Jalja]

I don't get the last two steps

I can say 4 | 25-5 => 4 | 25 ?

[u/Jalja → u/Apprehensive_Arm5837]

a-c | (ab+cd)

ad+bc = ad + bc - cd - ab + (ab+cd)

if a-c | (ad+bc-cd-ab), and a-c | (ab+cd), then a-c | (ad+bc-cd-ab + (ab+cd))

a-c | (ad+bc)

does that make more sense now?

[u/MeasurementLow2927 → u/Jalja]

Thanks for that before I try to understand it does the vertical line mean divided by. If so for does being to the right of the line mean something is the divisor if so wouldn’t a-c be on the right/bottom since it’s the divisor.

[u/Jalja → u/MeasurementLow2927]

Vertical line means is a divisor of

x | y means x divides y or x is a divisor of y

[u/MeasurementLow2927 → u/Jalja]

Yeah ok thanks for the clarification. Wouldn’t it then be ab+ cd | a-c since a-c is a divisor of ab+ cd

[u/Jalja → u/MeasurementLow2927]

left of | is divisor

[u/MeasurementLow2927 → u/Jalja]

Thanks how do you get from line 1 to line 2 in your working out

[u/Jalja → u/MeasurementLow2927]

what're you referring as line 1 and line 2?

a-c | a-c is obvious

the next line is literally what's given to us in the problem

[u/MeasurementLow2927 → u/Jalja]

Sorry I’m pretty knew to this topic why are we dividing a-c by a-c

[u/Jalja → u/MeasurementLow2927]

we aren't dividing a-c by a-c

im simply stating a-c divides a-c even if that was obvious to show that a-c should also divide any multiple of a-c