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Number Theory Level 2

The number of positive integral solutions of x 2 − y 2 = 9876543210 x^{2}-y^{2}=9876543210 is:


The answer is 0.

Fake Human by Fake Human , 21, India

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1 solution

Fake Human
Nov 29, 2017

x 2 − y 2 = ( x + y ) × ( x − y ) = 9876543210 x^{2}-y^{2}=(x+y)\times (x-y) =9876543210

9876543210 has only one even factor at a time

If x + y = o d d x+y=odd then x − y = e v e n x-y=even or vice a versa

2 x = o d d 2x=odd in either case, hence no positive integral solutions

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