document.write( "Question 393105: If n is a positive integer such that 2n+1 is a perfect square, show that n+1 is the sum of two successive perfect squares \n" ); document.write( "
Algebra.Com's Answer #279046 by Edwin McCravy(20060)\"\" \"About 
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If n is a positive integer such that 2n+1 is a perfect square, show that n+1 is the sum of two successive perfect squares.
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document.write( "Since 2n + 1 is odd, then since 2n + 1 is a perfect square, \r\n" );
document.write( "its square root is also odd, say 2p + 1, where p > 0, then\r\n" );
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document.write( " 2n + 1 = (2p + 1)²\r\n" );
document.write( " 2n + 1 = 4p² + 4p + 1\r\n" );
document.write( "     2n = 4p² + 4p\r\n" );
document.write( "      n = 2p² + 2p\r\n" );
document.write( "      n = p² + p² + 2p\r\n" );
document.write( "  n + 1 = p² + p² + 2p + 1\r\n" );
document.write( "  n + 1 = p² + (p + 1)²\r\n" );
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document.write( "Edwin
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