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document.write( "An arithmetic series of 30 375 terms has a sum that is a perfect fifth power. What is the smallest positive sum of this series?
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document.write( "The sum of this AP should be an integer positive number, which is a perfect fifth power.\r\n" );
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document.write( "The smallest integer positive number, which is a perfect fifth power is 1: 1 = 
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document.write( " I want to create an AP with 30375 terms, whose sum will be 1.\r\n" );
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document.write( "I will take c = 
as the central term of this AP.\r\n" );
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document.write( "I will take an arbitrary real number d as the common difference of this AP.\r\n" );
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document.write( " | I will take 15187 terms of this AP on the right from \"c\" |\r\n" );
document.write( " | and 15187 terms of this AP on the left from \"c\". |\r\n" );
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document.write( " 15187 is a remarkable number for this problem: \r\n" );
document.write( " it is about half of the number 30375.\r\n" );
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document.write( "When I will calculate the sum, the pairs of numbers c+kd and c-kd, equally remoted from the center, \r\n" );
document.write( "will give the sum of 2c; the parts \"+kd\" and \"-kd\" will cancel.\r\n" );
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document.write( "So, the sum of this my progression will be \r\n" );
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document.write( " central term c + 15187*(2c), or c*(1+2*15187) = 30375*c = 
= 1.\r\n" );
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document.write( " Thus, this AP will provide the answer: central term c = \r\n" );
document.write( " and the common difference d = an arbitrary real number.\r\n" );
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document.write( " You should take 15187 terms on the right from \"c\" \r\n" );
document.write( " and the same number, 15187 terms, on the left from \"c\".\r\n" );
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document.write( "The sum of all terms of this AP will be 1, which is the smallest positive integer perfect fifth power.\r\n" );
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document.write( "So, all the requirements are satisfied, and the solution is complete.\r\n" );
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document.write( "Solved.\r
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document.write( "Post-solution note:
Edwin constructed a degenerated AP with the zero common difference.\r
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document.write( " I constructed infinitely many APs with arbitrary value of the common difference.\r
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