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## Main Question or Discussion Point

Hello,

I'm playing with a set of quadratics x^2 + bx + c, where b is fixed, and c is allowed to be any integer image of a particular exponential function. As a simplistic example, I might have

x^2 + 100x + 3

x^2 + 100x + 9

x^2 + 100x + 27

x^2 + 100x + 81

etc.

and I'm trying to show that at least one of these quadratics has integer roots. Has anyone seen any results along these lines that might help?

Note that these are not the exact b's and c's I'm working with, it's only a simplistic example. I'm just looking for anything with a similar "flavor".

Approx

I'm playing with a set of quadratics x^2 + bx + c, where b is fixed, and c is allowed to be any integer image of a particular exponential function. As a simplistic example, I might have

x^2 + 100x + 3

x^2 + 100x + 9

x^2 + 100x + 27

x^2 + 100x + 81

etc.

and I'm trying to show that at least one of these quadratics has integer roots. Has anyone seen any results along these lines that might help?

Note that these are not the exact b's and c's I'm working with, it's only a simplistic example. I'm just looking for anything with a similar "flavor".

Approx

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