djb86 wrote: On a faded piece of paper it is possible to read the following: \[(x^2 + x + a)(x^{15}- \cdots ) = x^{17} + x^{13} + x^5 - 90x^4 + x - 90.\] Some parts have got lost, partly the constant term of the first factor of the left side, partly the majority of the summands of the second factor. It would be possible to restore the polynomial forming the other factor, but we restrict ourselves to asking the following question: What is the value of the constant term $a$? We assume that all polynomials in the statement have only integer coefficients. Setting $x=0$, we get $a|90$ Setting $x=-1$, we get $a|184$ and so $a|\gcd(90,184)=2$ and so $a\in\{-2,-1,1,2\}$ Setting $x=1$, we get $a+2|176$ and so $a\in\{-1,2\}$ Setting $x=2$, we get $a+6|137768$ and so the only possibility $\boxed{a=2}$