A number theory problem by Srini Sundaravaradhan

Number Theory Level 3

Find the number of pairs of positive integers ( x , y ) (x,y) satisfying x 2 − y 2 = 353702 x^2-y^2 = 353702 .

2 0 Infinite 1

Srini Sundaravaradhan by Srini Sundaravaradhan , 28, India

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2 solutions

(x+y)(x-y) = 353702 (2 x 17 x 101 x 103)

but observe that there is only one even number and hence one of (x+y), (x-y) is even and other is odd,hence no integral solution exists.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Viki Zeta
Oct 11, 2016

Pretty easy solution, draw the graph of hyperbola.

No solution exists, they never touch each other.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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