perplexus.info :: Just Math : Confirm or negate

Confirm or negate (Posted on 2020-04-24)

There is no polynomial P(x) with integer coefficients such that P(7)=11 and P(11)=13.

Prove or provide a counterexample.

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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Proof

| Comment 2 of 11 |

P(x) = Sum_k a_k x^k

and assume

P(11) - P(7) = 13 - 11 = 2 = Sum a_k(11^k - 7^k)

But 11^k - 7^k is divisible by 4, whereas 2 is not.

Posted by FrankM on 2020-04-26 21:14:00

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