This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 2

2024 Israel National Olympiad (Gillis), P2
Tags: number theory , remainders , fractional part , national olympiad
A positive integer $x$ satisfies the following: \[\{\frac{x}{3}\}+\{\frac{x}{5}\}+\{\frac{x}{7}\}+\{\frac{x}{11}\}=\frac{248}{165}\] Find all possible values of \[\{\frac{2x}{3}\}+\{\frac{2x}{5}\}+\{\frac{2x}{7}\}+\{\frac{2x}{11}\}\] where $\{y\}$ denotes the fractional part of $y$.

1976 Euclid, 4
Tags: remainders , polynomial division , algebra , polynomial
Source: 1976 Euclid Part B Problem 4 ----- The remainder when $f(x)=x^5-2x^4+ax^3-x^2+bx-2$ is divided by $x+1$ is $-7$. When $f(x)$ is divided by $x-2$ the remainder is $32$. Determine the remainder when $f(x)$ is divided by $x-1$.