Prime number and the coefficients of polynomial

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The discussion centers on the equation p = a(r - 1), where p is a prime number, r is a positive integer, and a is a constant. It concludes that the constant a can take specific values: either a = 1 with r = p + 1 or a = p with r = 2. The conversation emphasizes the relationship between prime numbers and their factors, confirming that prime numbers have only two distinct positive divisors: 1 and themselves. This relationship is crucial for understanding the implications of the equation in the context of modular arithmetic.

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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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