A family member of mine is currently taking high school Algebra 2 and is learning about the basics of modular arithmetic. The following question was asked of the students:
Find all integers n that satisfy the following:
$90\equiv 6 \pmod n$
The family member asked me for help, as she was stuck. But I too was stumped. It has been two years since I took Algebra 2, and I barely remember modular arithmetic. I seem to remember that $90\equiv 6 \pmod n$ means that 90 mod n = 6 mod n -- however, I am not sure how that can help me solve the problem.
I know this is a rather elementary question so I apologize if it has already been answered. That said, I have not been able to find an answer so far, as most sources deal with equations where the unknown value is something other than the one "inside" the mod parenthesis.
$90\equiv6\pmod n$ means $n$ divides $90-6,$ so the solutions for $n$ are the factors of $84.$