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**ElizabethMcArthur****Member**- Registered: 2016-09-20
- Posts: 1

I would appreciate it if someone could help me with this proof that I should perform. The task says:

If f(x) is a polynomial with integer coefficients, and if f(a)=f(b)=f(c)=-1, where a,b,c are three unequal integers, the equation f(x)=0 does not have integer solutions. Prove!

I know that if polynomial f(x) has integer coefficients and if it has integer solutions then that same solutions are divisors of coefficient that does not have x next to it. Now, I do not know how to include this with all the information that I got.

My homework solvers:

math - math helper

algebra - algebra helper

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 693
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We can write

[list=*]

[*]

[/list]

where *g*(*x*) is a polynomial with integer coefficients. If there were an integer solution, say *f*(*n*) = 0, then

[list=*]

[*]

[/list] since they are all integers. But if

Thus *f*(*x*) = 0 cannot have an integer solution.

Me, or the ugly man, whatever (3,3,6)

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