document.write( "Question 1110336: find all ordered pairs of integers (x, y) such that :
\n" ); document.write( " x^3 = 89x+40y
\n" ); document.write( " y^3 = 89x+40y \n" ); document.write( "

Algebra.Com's Answer #725334 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "1.  Right sides are identical  ====>  hence, left sides are equal:\r\n" );
document.write( "\r\n" );
document.write( "    x^3 = y^3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  Since x and y are integer, the last equality implies  x = y.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.  Then the either of the two given equations is equivalent to\r\n" );
document.write( "\r\n" );
document.write( "    x^3 = 89x + 40x,   or\r\n" );
document.write( "\r\n" );
document.write( "    x^3 = 129x,\r\n" );
document.write( "\r\n" );
document.write( "    x*(x^2-129) = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    In integer numbers, the last equation has only one solution  x= 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The only solution to the original system in integer numbers is the pair (x,y) = (0,0).\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );