# 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!

×