Guest Posted August 16, 2008 Report Share Posted August 16, 2008 There are exactly four positive integers in existence that are equal to the sum of the cubes of their digits ... Can you find them ? P.S. This is kind of like the inverse of Ben Law's problem here. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 16, 2008 Report Share Posted August 16, 2008 Hope I did got the problem right. Found 2, but it seems there are more then 4. 153 and 1 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2008 Report Share Posted August 17, 2008 Hope I did got the problem right. Found 2, but it seems there are more then 4. 153 and 1 You got it wrong .... 153 => 1+5+3=9 => 9*9*9= 729 and 153 is not equal to 729 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2008 Report Share Posted August 17, 2008 Hope I did got the problem right. Found 2, but it seems there are more then 4. 153 and 1 You got it wrong .... 153 => 1+5+3=9 => 9*9*9= 729 and 153 is not equal to 729 Ostap, you are correct in both cases. 1 is actually not a number I considered in the "exactly 4" from the OP, but it is 100% correct, so there are actually 5 and you have found 2. Ben, you mixed up the sum and cubing steps. 153 => 1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153 Quote Link to comment Share on other sites More sharing options...
0 Prime Posted August 17, 2008 Report Share Posted August 17, 2008 What do you mean only 4? I found 6. 0 = 03 1 = 13 153 = 13 + 53 + 33 370 = 33 + 73 + 03 371 = 33 + 73 + 13 407 = 43 + 03 + 73 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2008 Report Share Posted August 17, 2008 What do you mean only 4? I found 6. 0 = 03 1 = 13 153 = 13 + 53 + 33 370 = 33 + 73 + 03 371 = 33 + 73 + 13 407 = 43 + 03 + 73 Yay, Prime found all four of mine, the "1" that I forgot about and was discussed earlier, and "0" isn't actually a positive integer so it doesn't really count. Quote Link to comment Share on other sites More sharing options...
0 Prime Posted August 17, 2008 Report Share Posted August 17, 2008 Yay, Prime found all four of mine, the "1" that I forgot about and was discussed earlier, and "0" isn't actually a positive integer so it doesn't really count. Is zero negative, or is it not an integer? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2008 Report Share Posted August 17, 2008 Is zero negative, or is it not an integer? I don't think it is negative OR positive. It is an integer though. In any case, Wolfram agrees that it is not a positive integer: http://mathworld.wolfram.com/PositiveInteger.html Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 17, 2008 Report Share Posted August 17, 2008 I got 153, 370, 371, and 407. Not sure if 1 is included because its too simple . Quote Link to comment Share on other sites More sharing options...
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There are exactly four positive integers in existence that are equal to the sum of the cubes of their digits ... Can you find them ?
P.S. This is kind of like the inverse of Ben Law's problem here.
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