document.write( "Question 1150079: If (a)(b^4)(c^3)=1215000, where a, b and c are distinct positive integers greater than 1, what is the greatest possible value of a+b+c. \n" ); document.write( "

Algebra.Com's Answer #771439 by ikleyn(52794) $\"\"$ $\"About$

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document.write( "The prime decomposition of the number 1215000 is\r\n" );
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document.write( "    1215000 = ...\r\n" );
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document.write( "Comparing it with  , you see that\r\n" );
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document.write( "    either  a= 3^5,  b= 5,    c= 2,      with  a+b+c = 3^5 + 5 + 2   = 250,\r\n" );
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document.write( "    or      a= 3^2,  b= 5,    c = 2*3,   with  a+b+c = 3^2 + 5 + 2*3 =  20,\r\n" );
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document.write( "    or      a = 3,   b= 5*3,  c = 2,     with  a+b+c = 3   + 5*3 + 2 =  20.\r\n" );
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document.write( "So, a+b+c is maximal and equal to 250  at  a= 3^5,  b= 5  and c= 2.    ANSWER\r\n" );
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