Modular arithmetic

E

egal

New member
Joined
Jul 13, 2021
Messages
33
How do we know 28! is congruent to 1 modulo 29? My book didn't give any way to calculate this
 
egal said:
How do we know 28! is congruent to 1 modulo 29? My book didn't give any way to calculate this
Click to expand...
Why do you think it is? I just used the Windows calculator, and it gave a different answer.

Without a calculator, doing it by hand, you could just multiply 28*27*..., reducing mod 29 at each step. Or you might have learned other shortcuts.

What has your book taught you about modular arithmetic?

If this is an exercise from that book, what topics are covered in that section, that you might be expected to use? And please quote the exercise exactly as given, including any instructions.
 
Dr.Peterson said:
Why do you think it is? I just used the Windows calculator, and it gave a different answer.

Without a calculator, doing it by hand, you could just multiply 28*27*..., reducing mod 29 at each step. Or you might have learned other shortcuts.

What has your book taught you about modular arithmetic?

If this is an exercise from that book, what topics are covered in that section, that you might be expected to use? And please quote the exercise exactly as given, including any instructions.
Click to expand...
I can't paste the exercise as it's written in Turkish. It turns out I didn't understand the solution, but I'm back to school so we'll work the exercise out with my teacher. I apologize for the late reply, thank you for your time
 
egal said:
I can't paste the exercise as it's written in Turkish. It turns out I didn't understand the solution, but I'm back to school so we'll work the exercise out with my teacher. I apologize for the late reply, thank you for your time
Click to expand...
Do you understand that:

28 ! = 1 * 2 * 3 *.......* 26 * 27 * 28

and 29 is a prime number.
 
egal said:
the division won't be an integer, there will be a remainder as 28! and 29 don't have a common divisor
Click to expand...
Seems to me we should consider whether 28!-1 is divisible by 29, not 28!.
 
egal said:
How do we know 28! is congruent to 1 modulo 29? My book didn't give any way to calculate this
Click to expand...
Look at this calculation: [imath]\dfrac{28!}{29}[/imath] SEE IT HERE
Do you see that [imath]28[/imath] is the the remainder if [imath]28![/imath] is divided be [imath]29~?[/imath]
Then by definition [imath]28![\mod 29]=28[/imath].

[imath][/imath][imath][/imath][imath][/imath][imath][/imath][imath][/imath][imath][/imath]
 
You must log in or register to reply here.
Top