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)

Comments: ( Back to comment list | You must be logged in to post comments.)

solution

| Comment 1 of 11

Plug in x=11 and x=7 and subtract the two equations.

Every term of the difference is integer*(11^k - 7^k) which is divisible by 11-7=4.

But the difference is 13-11=2 which is not divisible by 4, so no such polynomial exists.

Posted by xdog on 2020-04-24 16:39:35

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info