MHB Prime number and the coefficients of polynomial

[anemone]

Hi,
I've got an equation stating p=a(r-1).
If p represents prime number and r is a positive integer, and a is a constant, what can we conclude for the constant a?
Like a $\in${-1, 1, -p, p}?
I suspect this has something to do with modular arithmetic...

Thanks.

 

[awkward]

About all we can say is that either
(1) a = 1 and r = p+1
or
(2) a = p and r = 2.

 

[HallsofIvy]

It has everything to do with the definition of "prime number"- a number whose only factors are 1 and itself. Thus giving awkwards response.