find atleast 7 solutions of the equation. 900x+7689y=109876 CAN ANYONE SOLVE THIS now lets find 7 integral solutions


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Question Number 84005 by redmiiuser last updated on 08/Mar/20

$f i n d a t l e a s t 7 s o l u t i o n s$ $o f t h e e q u a t i o n .$ $900 x + 7689 y = 109876$ $C A N A N Y O N E S O L V E$ $T H I S$ $n o w l e t s f i n d 7 i n t e g r a l$ $s o l u t i o n s$
Commented by redmiiuser last updated on 08/Mar/20

$i a s k e d t o f i n d 7 s o l u t i o n s$
Commented by Rio Michael last updated on 08/Mar/20
$or you could use bezouts identity to find the general solution and substitude for some integer λ gen sol: { ((x = x_0 + ((7689)/d)λ)),((y = y_0 −((900)/d)λ)) :} where d = gcd(900,7689)$
$or you could use$ $bezouts identity to$ $find the general solution$ $and substitude for some integer λ$ $g e n s o l : {\begin{cases} x = x_{0} + \frac{7689}{d} λ \\ y = y_{0} - \frac{900}{d} λ \end{cases}$ $w h e r e d = g c d (900, 7689)$
Commented by mr W last updated on 08/Mar/20

$t h e r e i s n o i n t e g r a l s o l u t i o n! s i n c e$ $g c d (900, 7689) = 3 \neq 1, t h a t m e a n s$ $L H S i s a l w a y s a m u l t i p l e o f 3, b u t$ $109876 i s n o t a m u l t i p l e o f 3 .$
Commented by Rio Michael last updated on 08/Mar/20

$thats a good point sir thanks$
	Answered by $@ty@m123 last updated on 08/Mar/20

	$A s t h e r e i s n o r e s t r i c t i o n s,$ $w e c a n p u t x = 1, 2, 3, . . . . . u p t o \infty$ $a n d f i n d c o r r e s p o n d i n g v a l u e s o f y .$
	Commented by redmiiuser last updated on 08/Mar/20

	$o k l e t s m a k e i t d i f f i c u l t$ $f i n d 7 i n t e g r a l s o l u t i o n s$
	Commented by redmiiuser last updated on 08/Mar/20

	$g i v e m e a q u i c k a n s w e r$
	Answered by redmiiuser last updated on 08/Mar/20

	$i t i s o b v i o u s t h a t t h e r e$ $a r e \infty s o l u t i o n s s i n c e$ $i t i s a s t r a i g h t l i n e$
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