$x^2 - y^2 = 2019$

Number Theory Level 2

Is it possible to express $2019$ as the difference between two perfect squares?

No Yes

2 solutions

Ossama Ismail
Dec 22, 2018

Ans: Yes

$x^2 - y^2 = (x+y)(x-y) = 2019$ has two solutions , $2019 = 3 \times 673 = 1 \times 2019$ . This gives $(x,y) = (338,335) \ \text{and} \ (1010 , 1009)$ .

Parth Sankhe
Dec 23, 2018

Difference between any two consecutive squares consist of all odd numbers i.e. 4-1=3, 9-4=5, 16-9=7, ...

Hence there will be some consecutive numbers whose difference of squares will be 2019

x 2 − y 2 = 2019 x^2 - y^2 = 2019 x 2 − y 2 = 2 0 1 9

2 solutions

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$x^2 - y^2 = 2019$