easy Pure Math

Full Solutions

A release-checked easy problem for training Pure Math.

Question

Find all pairs of integers $(x,y)$ such that $3x + 7y = 10000$. All of the solutions can be written in the form $x = a + 7n$ and $y = b - 3n$, where $n$ is any arbitrary integer and $a,b$ are integers such that $b$ is a minimal positive integer. Find $ab$.

Practice focus

This Pure Math problem is tagged Pure Math. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.