$\frac 1{2013}=\frac 1 x - \frac 1 y \\ x=\frac{2013y}{y+2013} \\ x=2013-\frac{2013^2}{y+2013} \\ y+2013 > 2013 \text{ olduğundan } x>0 \text{ olur.} \\ 2013^2=3^2.11^2.61^2\\ t=y+2013, 2013^2\text{'nin bir çarpanı olduğundan, } \frac 1 x=\left( 2013- \frac{2013^2}{t}\right )^{-1} \text{ ve } \\ \frac 1y=\frac 1{t-2013} \text{ olarak tüm eşitlikler aşağıdaki gibi yazılabilir. } \\ $
| $2013-x$
|
$2013+y$
|
$x$
|
$y$
|
$\frac 1 {2013}=$
|
| $1$
|
$4052169$
|
$2012$
|
$4050156$
|
$\frac 1 {2012}- \frac 1 {4050156}$
|
| $3$
|
$1350723$
|
$2010$
|
$1348710$
|
$\frac 1 {2010}- \frac 1 {1348710}$
|
$3^2=9$
|
$450241$
|
$2004$
|
$448228$
|
$\frac 1 {2004}- \frac 1 {448228}$
|
$11$
|
$368379$
|
$2002$
|
$366366$
|
$\frac 1 {2002}- \frac 1 {366366}$
|
$3.11=33$
|
$122793$
|
$1980$
|
$120780$
|
$\frac 1 {1980}- \frac 1 {120780}$
|
$61$
|
$66429$
|
$1952$
|
$64416$
|
$\frac 1 {1952}- \frac 1 {64416}$
|
$3^2.11=99$
|
$40931$
|
$1914$
|
$38918$
|
$\frac 1 {1914}- \frac 1 {38918}$
|
$11^2=121$
|
$33489$
|
$1892$
|
$31476$
|
$\frac 1 {1892}- \frac 1 {31476}$
|
$3.61=183$
|
$22143$
|
$1830$
|
$20130$
|
$\frac 1 {1830}- \frac 1 {20130}$
|
$3.11^2=363$
|
$11163$
|
$1650$
|
$9150$
|
$\frac 1 {1650}- \frac 1 {9150}$
|
$3^2.61=549$
|
$7381$
|
$1464$
|
$5368$
|
$\frac 1 {1464}- \frac 1 {5368}$
|
$11.61=671$
|
$6039$
|
$1342$
|
$4026$
|
$\frac 1 {1342}- \frac 1 {4026}$
|
$3^2.11^2=1089$
|
$3721$
|
$924$
|
$1708$
|
$\frac 1 {924}- \frac 1 {1708}$
|