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!

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