MHB Prime number and the coefficients of polynomial

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The equation p = a(r - 1) relates a constant a, a positive integer r, and a prime number p. The discussion concludes that a can either be 1 with r equal to p + 1, or a can be p with r equal to 2. The relationship is tied to the definition of prime numbers, which are only divisible by 1 and themselves. The conversation hints at a connection to modular arithmetic but does not delve deeply into that aspect. Overall, the exploration of the equation reveals limited possible values for the constant a in relation to prime numbers.
anemone
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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...:confused:

Thanks.
 
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About all we can say is that either
(1) a = 1 and r = p+1
or
(2) a = p and r = 2.
 
It has everything to do with the definition of "prime number"- a number whose only factors are 1 and itself. Thus giving awkwards response.
 

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