concerning the value of 1∙2∙3∙∙∙(p-1)+1 in p-hour clock arithmetic, where p is a prime number?

Question

What would be a legitimate conjecture for this problem? (Suggestion: Consider a number of examples using the first few primes)

Answer 1

To see what conjecture they are interested in, it really is necessary to consider a number of examples, exactly as they said. So lets set up a table. We will call the product in question N.
Remember that we are only interested in prime numbers for p.

p N N/p
---------------------------------
2 2 1
3 3 1
5 25 5
7 721 103
11 3628801 329891
13 479001601 36846277

Notice that the numbers N so far have all been divisible by p. So, if we represented them on a p-clock, they would all be p o'clock (or 0 o'clock if you prefer). That is the conjecture they are interested in. You are supposed to conjecture that the value of 1*2*3*...*(p-1)+1 in p-hour arithmetic is always p o'clock.

Answer 2

ok im dumb, but if p=3 then !,!!
! !
!! !
!
or one onetwo lol.
probably wrong tune to be dancing to huh?
first glance it seemed like groundhog day, until (i think the equation said present is = to (p-1)+1
but hey er hay, im just a highschool barely made it. fte, nice sticker or
"1 day at a time"
"live life on your terms, not lifes, because life will keep you in park" but fte all the same.