Question

Find the number of positive integral solutions of the equation xy = 2^300​

Answer 1

Step-by-step explanation:

30We have (x+y)*(x-y)=300

Also

300=1*300

=2*150

=3*100

=4*75

=5*60

=6*50

=10*30

=12*25

=15*20

As x and y are integers their sum of their sum and difference is always even.

i.e. (x+y)+(x-y) is even..

This happens only in case of

2*150

6*50

10*30

Solving which we have the pair of

76,74

28,22

20,10