Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Logic and Integers.
Let P denotes the set of all positive integers and \(S={(x,y):x\in P,y \in P} and x^{2}-y^{2}=666\) The number of distinct elements in the set is
Logic
Relations
Integers
Answer: 0
B.Stat Objective Question 73
Challenges and Thrills of Pre-College Mathematics by University Press
\(x^{2}-y^{2}=666\) for all pairs of factors of 666
1 and 666, 2 and 333, 6 and 111, 9 and 74, 18 and 37 such that given condition holds
x and y are non integers then number of distinct elements in the set in the set is 0.
I.S.I. & C.M.I. Entrance Program
Taught by students and alumni of I.S.I. & C.M.I.
