document.write( "Question 1162749: If g(x) = x + x^2, prove that g(n) − 4g(m) = 0 has no solutions for positive integers m and n. \n" ); document.write( "

Algebra.Com's Answer #786611 by ikleyn(52908) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " Obviously, this problem is EITHER for advanced school (?) students OR for not-indifferent amateurs.\r
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\n" ); document.write( "\n" ); document.write( " Therefore, I will give only the idea of the proof, without going into details.\r
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document.write( "(1)  It is \"almost obvious\", that the best (most closest) approximation to 4g(m) by the numbers of the form  n+n^2 = n*(n+1)  is  g(2m).\r\n" );
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document.write( "     It can be checked by analyzing inequalities . . . \r\n" );
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document.write( "(2)  At the same time, it is easy to check manually that  g(2m)  is not equal to 4g(m).\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is how I see the possible proof . . . \r
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