I have to find out the number of positive integral solutions $(x,y)$ of
Specifically, if $S$ is the set of all ordered pairs $(x,y)$ then $S$ -
A) is an infinite set
B) is the empty set
C) has exactly one element
D) is a finite set and has at least two elements.
Now, with a calculator capable of doing prime factorization, this is an easy question. However without a calculator, its very difficult to find the prime factors by inspection. What is the most efficient and fast solution to such a question.
This question was asked here (Q no. 4)