Modular arithmetic: i wanted to ask whether the interpreation of X = 361 + 1(mod461 +1) the same as X=362(mod462).

[elioruzan]

hi.
i wanted to ask whether the interpreation of X = 361 + 1(mod461 +1) the same as X=362(mod462). and if not, what exactly does it mean.
thank you.

 

[Dr.Peterson]

hi.
i wanted to ask whether the interpretation of X = 361 + 1(mod461 +1) the same as X=362(mod462). and if not, what exactly does it mean.
thank you.
View attachment 37484

That's the only reasonable interpretation I can see for it.

But where in the world did you see such a statement? Can you show us the context?

 

[elioruzan]

from my online college exam about chinese remainder theorem (advanced algebra)

 

[elioruzan]

here is the question, i will translate: find a solution for the following system:
obviously I am not looking for an answer, just interpretation and possibly conventional notations.
thank you for helping me.

 

[blamocur]

View attachment 37485here is the question, i will translate: find a solution for the following system:
obviously I am not looking for an answer, just interpretation and possibly conventional notations.
thank you for helping me.

I assumed that the second condition means [imath]x \equiv 362 (\mod 462)[/imath], and my script found only one such solution for [imath]461^2<x<2\cdot 461^2[/imath]

 

[Dr.Peterson]

from my online college exam about chinese remainder theorem (advanced algebra)

In that context, I think it's clear it is intended to mean the only thing it really can mean, because that makes sense. It would appear they just want to emphasize that both numbers have been increased by 1.