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Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Logic and Integers.

## Logic and Integers (B.Stat Objective problems)

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

• 1
• 0
• 2
• more than 2

### Key Concepts

Logic

Relations

Integers

But try the problem first…

Source

B.Stat Objective Question 73

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

$x^{2}-y^{2}=666$ for all pairs of factors of 666

Second Hint

1 and 666, 2 and 333, 6 and 111, 9 and 74, 18 and 37 such that given condition holds

Final Step

x and y are non integers then number of distinct elements in the set in the set is 0.