Y? ($X,Y,Z \in \mathbb{N}$)

Asked Aug 22 '20 at 12:31

Active Aug 22 '20 at 13:46

Viewed 62 times

I'm not sure how to prove/disprove this. I tried using the fact that $(A + B) \bmod C = (A \bmod C + B \bmod C) \bmod C$ or writing this as $X-Y \neq Zk$ but it doesn't seem very helpful. I tested a lot of numbers and it seems true.

edited Aug 22 '20 at 13:46

asked Aug 22 '20 at 12:31

Dawid

Your notation is unclear. Use brackets to clarify the first line. – Chrystomath Aug 22 '20 at 13:36
Didn't realise it could be unclear. Added brackets. Thanks! – Dawid Aug 22 '20 at 13:48
Isn't it obvious? If $(X\mod{Z})=Y$ then $(X\mod{Z})=(Y\mod{Z})$. What am I missing? – Chrystomath Aug 22 '20 at 13:53
I'm not sure what you mean. This seems different than what i wrote. I wrote that if $((X-Y) \bmod Z) \neq 0$ then $(X \bmod Z) \neq Y$ – Dawid Aug 22 '20 at 14:12
It's the contravariant statement. If NOT $A\implies$ NOT $B$ then equivalently, $B\implies A$. – Chrystomath Aug 23 '20 at 05:20

Does $(X-Y) \bmod Z \neq 0$ imply that $X \bmod Z \neq Y$ if (X-Y)>Z>Y? ($X,Y,Z \in \mathbb{N}$)

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