$100+ day streak problem$

Number Theory Level 2

If $x^2 = y^2 + 1457$ , find $x\times y$ if $x$ and $y$ are positive integers each less than 100.

3 solutions

Majed Musleh
May 28, 2015

$(x^{2}) -(y^{2})=1457$

$*(x-y)(x+y)=(31)*(47)*$

$*(x-y)=31....(1)*$

$*(x+y)=47...(2)*$

$*adding (1)+(2)*$

$*2x=78*$

$*x=39*$

$*y=8*$

$*Note* : if *we* take* (x-y)=47* and* (x+y)=31*$

$*y* will *have* a negative *value*$

nice solution!!!

samuel ayinde - 6 years ago

Sujith Kumar
Sep 3, 2015

I have another solution in mind : x=729 and y=728

Ramiel To-ong
Jun 8, 2015

only 39 and 8 will satisfy for the given condition