# Pears and Undiscovered Homophones!

**Number Theory**Level pending

Define *Pearity* as if a positive integer is \( 1 (mod 4) \) or \( 2 (mod 4) \), or if it is \( 3 (mod 4) \) or \( 0 (mod 4) \). If it is the former, define the integer to be *Bosc*, and if it is the latter, define the integer to be *Bartlett*. Take a *Bosc*. Divide it by \( n \), and get a *Bartlett*. Then divide it by \( n+1 \) and get another *Bosc*. Divide by \( n+2 \) and get \( p \) (a *Bartlett*). \( p \) is a prime from \( 30 \) to \( 40 \). Find if n is a *Bartlett*. DON'T GUESS!

*Pearity* is a *Parody* of *Parity*. Cool!