1070.23 – State a Theorem

State a theorem about the integers but not just any old theorem. Arrange that yours is valid for all integers nn except 5, 17, and 257. (Hint: There are many reasons why equations fail. There are also such things as inequalities.)

Solution

There are many possible answers. Here are two.

(x−5)(x−17)(x−257)≠0(x-5) (x-17) (x - 257) \neq 0

(x−5)(x−17)(x−257)(x−5)(x−17)(x−257)=1 \dfrac{(x-5) (x-17) (x - 257)}{(x-5) (x-17) (x - 257)} = 1