100 + d a y s t r e a k p r o b l e m 100+ day streak problem

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


The answer is 312.

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3 solutions

Majed Musleh
May 28, 2015

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

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

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

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

a d d i n g ( 1 ) + ( 2 ) *adding (1)+(2)*

2 x = 78 *2x=78*

x = 39 *x=39*

y = 8 *y=8*

N o t e : i f w e t a k e ( x y ) = 47 a n d ( x + y ) = 31 *Note* : if *we* take* (x-y)=47* and* (x+y)=31*

y w i l l h a v e a n e g a t i v e v a l u e *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

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