### Questions (121)

 11 How to prove this inequality involving the minimum of two chosen numbers 7 Help in solving a simple functional equation 7 Help in solving this geometry problem 7 Show that $n ≤ 100$ if $\{A_1,A_2,… ,A_n\}$ is a set of distinct $3$-element subsets of $\{1, 2,… , 36\}$ such that… 6 How to solve this number theory question from INMO?

### Reputation (1,091)

 +5 Prove that if $f(x)$ is a polynomial having real coefficients such that $F(x) = f(x^3) + xg(x^3)$ and $F(x)$ is divisible by $x^2 + x + 1$. +5 Proving that $\left\{ \frac{sm}{p} \right\} < \left\{ \frac{sn}{p} \right\} < \frac{s}{p}$ if and only if $s\not\mid p-1$ +5 Help in solving a simple functional equation -2 Help in solving the geometry question

 3 How many ways are there to form a sequence of 10 letters from 4 a's, 4 b's, 4 c's, and 4 d's if each letter must appear twice? 1 How can I prove that $R$ is an equivalence relation in $A$?

### Tags (64)

 3 combinatorics × 18 0 elementary-number-theory × 12 1 discrete-mathematics 0 polynomials × 11 0 geometry × 35 0 sequences-and-series × 9 0 triangles × 17 0 inequality × 7 0 contest-math × 17 0 number-theory × 6