## 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:

$714653289 \; = \; 26733^2$

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

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

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

math grad - Interest: Number theory
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### 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.