This question is inspired from a earlier post on this forum.
Prove that if
x.y = -1 mod 24
x = -y mod 24.
Is there a smart way to do this? All I could do was enlist the distinct values for x,y and prove the above for each such pair.
Thanks Tonio. I am afraid I did not understand everythign you said (I have limited exposure to Group Theory)
What you must be saying is that ans to my question is direct application of the fact you wrote. But is there a way to do it understand it without relying on this.
I will tell you my approach - I found all pairs of x,y (between 0 and 23) for which the first condition is satisfied. Then checked the result to be proved for each such case. And hence satisfied my self with it.
But I'm not too happy with this approach. What if instead of 24 - I had a a bigger number? Is 24 the only number that satisfies this - are there others? If yes - what is the criteria etc? (I know for sure there are a few more numbers like that). So, these are the questions I am struggling to answer.
Any direction / input will be great.