Integral solutions of
Number Theory
Level
3
Find the number of pairs of nonnegative integers satisfying
0
2
1
4
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Answer is 1
a 2 + b 2 = a 2 b 2
a 2 b 2 − a 2 − b 2 = 0
a 2 b 2 − a 2 − b 2 + 1 = 1
a 2 ( b 2 − 1 ) − ( b 2 − 1 ) = 1
( a 2 − 1 ) ( b 2 − 1 ) = 1
The only integral solution to the above equation is a = b = 0