A friend of us makes up a polynomial with nonnegative integer coefficients. Our task is to find it out with a minimum number of queries. For each query we give him a nonnegative integer $L$ and he computes $P(L)$ and returns the result to us.
I know the beautiful trick to solve this - first ask $P(1)$ to determine the sum of the coefficients that is at least as great as the greatest coefficient of the polynomial. Let $T$ be the result of $P(1)$. Then we ask $P(T + 1)$. The value we get we convert to a $T + 1$-base positional system and this way we figure the coefficients of the polynomial in 2 queries. I was wondering if it is possible to find it with a single query or 2 queries is the lower bound of the worst case?