document.write( "Question 891401: What is the largest 3-digit-number with the property that the number is equal to the sum of its hundreds digit, the squared of its 10 digit and the cube of its units digit? \n" ); document.write( "

Algebra.Com's Answer #539726 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
There isn't a really nice analytic solution other than casework on the units digit (which is still painfully time-consuming). I wrote a small Python program that checks all possibilities (add indentations):\r
\n" ); document.write( "\n" ); document.write( "def solve():
\n" ); document.write( " a = 1
\n" ); document.write( " b = 0
\n" ); document.write( " c = 0
\n" ); document.write( " for a in range(1, 10):
\n" ); document.write( " for b in range(0,10):
\n" ); document.write( " for c in range(0,10):
\n" ); document.write( " if 100*a + 10*b + c == a + b**2 + c**3:
\n" ); document.write( " print 100*a + 10*b + c
\n" ); document.write( " return None\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The solutions are 135, 175, 518, and 598, the largest of which is 598. \n" ); document.write( "

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