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The article talks about cases where a quadratic "polynomial factorizes and therefore produces composite numbers as x takes the values 0, 1, 2, ..." but I'm curi
by dane-pgp 5y ago
The article talks about cases where a quadratic "polynomial factorizes and therefore produces composite numbers as x takes the values 0, 1, 2, ..." but I'm curious about other cases when a polynomial produces only composite numbers.
In particular, can we find or test single-variable polynomials that produce an infinite number of different values, which don't all share a common factor, but which are all composite numbers (except possibly some primes near the start)?
- yesenadam 5y ago> single-variable polynomials that produce an infinite number of different values, which don't all share a common factor, but which are all composite numbers How about x^2 ?
- dane-pgp 5y agoThat's a great simple example, thank you.
- mkl 5y agoNo common factors at all between any of the values, or no factor common to all the values? The second is pretty straightforward, e.g. (x+1)*(x+3) produces 3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323, 360, 399, etc. for x = 0, 1, 2, ....
- dane-pgp 5y agoGood point, thank you! For some reason it didn't occur to me that such a polynomial would generate values like 143 = 11 * 13.