Algebra.Com's Answer #633408 by ikleyn(52802)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "If a, b, c are odd integers, then the equation  has no FRACTION solution. \r
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document.write( "I know how to prove, if it said integer solution, but to prove that theres no fraction solution, it seems a little hard for me. \r
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document.write( "Im really sorry if its the wrong section\r
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document.write( "Thanks~!
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document.write( "Assume the equation  =  with odd integer coefficients a, b an c has the solution, \r\n" );
document.write( "which is a rational fraction  with integer p and q. \r\n" );
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document.write( "We can assume that all the common divisors of p and q are just canceled in the fraction , \r\n" );
document.write( "so that p and q are relatively primes integer numbers. In particular, p and q are not both multiples of 2 simultaneously.\r\n" );
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document.write( "Then substitute the fraction into the equation.\r\n" );
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document.write( "You will get  = .\r\n" );
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document.write( "Multiply both sides by  to rid off the denominators. You will get\r\n" );
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document.write( " = . (1)\r\n" );
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document.write( "Now, if p is odd, then q can not be multiple of 2, otherwise you easily get a contradiction due to equation (1).\r\n" );
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document.write( "Similarly, if q is odd, then p can not be multiple of 2, otherwise you easily get a contradiction due to equation (1).\r\n" );
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document.write( "Thus both p and q must be odd. \r\n" );
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document.write( "Then the equation (1) has three odd addends that sum up to zero, which is impossible.\r\n" );
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document.write( "This contradiction completes the proof.\r\n" );
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