document.write( "Question 1037770: N and p are integers greater than one. 5n is the square of
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Algebra.Com's Answer #652415 by Edwin McCravy(20055)\"\" \"About 
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N and p are integers greater than one. 5n is the square of
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75∙n∙p = (3∙5∙5)∙n∙p = 3∙5∙(5∙n)∙p = \r\n" );
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document.write( "[5∙n must be the square of an integer, and that will be\r\n" );
document.write( "the case if n contributes an odd number of factors of 5.\r\n" );
document.write( "So we try n as just 1 factor of 5, i.e., n=5] \r\n" );
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document.write( "75∙n∙p = 3∙5∙(5∙5)∙p = 3∙(5∙5∙5)∙p\r\n" );
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document.write( "[That has 3 factors of 5, and thus the whole thing will be the \r\n" );
document.write( "cube of an integer if p contributes 2 more factors of 3.\r\n" );
document.write( "So we take p = 3∙3]\r\n" );
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document.write( "75∙n∙p = 3∙(5∙5∙5)∙p = 3∙(5∙5∙5)∙(3∙3) = (3∙3∙3)(5∙5∙5) = 3³∙5³\r\n" );
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document.write( "So n = 5, p = 3∙3 = 3² = 9\r\n" );
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document.write( "Checking:  5∙n = 5∙5 = 25 = 5² \r\n" );
document.write( "          75∙n∙p = 75∙5∙9 = 3375 = 15³\r\n" );
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document.write( "n+p = 5+9 = 14.\r\n" );
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document.write( "Edwin
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