No this isn't for a silly math exercise, it's a relationship with a hottie I don't want to lose at stake:
I like my TV volume to be on Perfect Squares, but she likes her volumes on Prime Numbers.
Easily provable is that for $n \geq 2$, there's no such number. $n = 0$ or $1$ are not prime numbers.
Mute is our current compromise, but for some programs that's just not feasible. If you're going to say "You're crazy/she's crazy", save it: I know.
I'm willing to stretch the rules to make this work. For example, my friends surround sound is actually measured in -dB, in which case -9 db would be a perfect volume (0 + 3i), both parts of that complex number satisfy one of us.
Is there any work arounds you guys can think of? Any crazy sketchy proof of why there exists a number (preferably positive, I dont wanna buy a new speaker system) that works for us?
Please Mathematics. This girl is out of my league beautiful, and into me.