A curious perfect square

 
 
 

There’s a perfect square – a permutation of the nine nonzero digits – which, when its units digit is removed, leaves an 8-digit number   N   with the properties that   9 \, N   contains the nine nonzero digits, and   18 \, N   contains the ten decimal digits.

Find that square.

 
 

Paul found:

 
714653289 \; = \; 26733^2

m \; = \; 71465328\not{9}

  9 \, m \; = \; 71465328 \; \times \; 9 \; = \; 643187952

18 \, m \; = \; 71465328 \; \times \; 18 \; = \;  1286375904

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

2 Responses to A curious perfect square

  1. paul says:

    The square is

    n = 714653289
    drop the 9 to give m = 71465328
    9 m = 643187952 with no zeros and 18 m = 1286375904

    Paul.

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