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Question Number 26438 by San Sophanethsan069 last updated on 25/Dec/17

	Answered by mrW1 last updated on 25/Dec/17

	$A = 999 . . . 9 (n d i g i t s 9)$ $S (A) = s u m o f d i g i t s o f A = 9 n$ $A = 10^{n} - 1$ $A^{2} = {(10^{n} - 1)}^{2} = 10^{2 n} - 2 \times 10^{n} + 1$ $A^{2} = (10^{n} - 2) \times 10^{n} + 1 = 999 . . . 98000 . . . 01$ $(n - 1 d i g i t s 9, o n e d i g i t 8, n - 1 d i g i t s 0, o n e d i g i t 1)$ $S (A^{2}) = 9 \times (n - 1) + 8 + 0 \times (n - 1) + 1 = 9 n$ $i . e . A a n d A^{2} h a v e t h e s a m e s u m o f$ $d i g i t s .$
	Commented by San Sophanethsan069 last updated on 26/Dec/17

	$Thank you so much$
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