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## Homework Statement

Let f(x) = ax^2 + bx + c be a quadratic polynomial. Either prove or disprove the following statement: If f(0) and f(1) are even integers then f(n) is an integer for every natural number n.

## Homework Equations

## The Attempt at a Solution

I tried different approaches such as analyzing the constants, f(n)-f(0)-f(1).

How do you approach these problems in general?