bluecarneal wrote: A student did not notice multiplication sign between two three-digit numbers and wrote it as a six-digit number. Result was 7 times more that it should be. Find these numbers. So $1000x+y=7xy$ $\iff$ $(7x-1)(7y-1000)=1000$ Divisors of $1000$ $\equiv -1\pmod 7$ are $20,125,1000$ giving as possibilities $(3,150),(18,144),(143,143)$ Hence the answer : $\boxed{(143,143)}$

Well, the problem has been recycled, as Problem 6, grade R8, at the (in)famous "Formula of Unity - Formulo de Integreco" mathematical olympiad 2014-2015. Such a pith!