This game is thanks to David Bedford at the BCME Conference in Warwick.
One person writes down a polynomial with positive integer coefficients. Call it f(x) They then choose an integer that it bigger than all their coefficients. Call it n. They then calculate f(n) and give just n and f(n) to the second person.
The second person should be able to name that polynomial! How?
Example:
Given only n=8 and f(n) = 6855 how could you work out that the polynomial was
?
It might help to think about an example when n=10 first.
in your example :
f(x)=x^4+5x^3+3x²-7
-7 is a minus coefficient…
-7x^0 …. but the method works only with a polynomial with positive integer coefficients, doesn’t it ?
That is a very good point! Thank you so much Keltouma Assal. I have changed it now.