True or False:

**64** is the only square the sum of whose digits less unity and product plus unity are squares

and, 3 + 5 = 8

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True or False:

**64** is the only square the sum of whose digits less unity and product plus unity are squares

and, 3 + 5 = 8

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%d bloggers like this:

False: 433 is the next number, which square follows the rules.

433^2 = 187489

(1+8+7+4+8+9) -1 = 36 = 6^2

(1*8*7*4*8*9)+1 = 16129 = 127^2

Other numbers below 100000 are: 728, 1727, 2483, 6769, 7435, 7721, 9269, 9442, 10691,10882, 13463,13535, 14966,15227, 20278, 21131, 24139, 24479, 25381, 29611, 30689, 34127, 35531, 38161, 40211, 40807, 42911, 47161, 50129, 52111, 57815, 59489, 74312, 90073, 97579

pipo

I found a lot like that Pipo, but in your first example 6 + 127 is not equal to 433, ( the last statement). I went to 1,000,000 and found none. This is the last one I found

{{3,6}, {1,6,1,2,9}, 6, 127, 133, 901189}

the 133 has to equal 901189 and is getting further behind at each part solution, I suspect there are no other solutions that meet all criteria.

Paul.

I overlooked the last criterium, so indeed you are right.

pipo