If in a number system 25×32=1163 find how many digits are there in the number system used.


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Question Number 140008 by ajfour last updated on 03/May/21

$I f i n a n u m b e r s y s t e m$ $25 \times 32 = 1163$ $f i n d h o w m a n y d i g i t s a r e t h e r e$ $i n t h e n u m b e r s y s t e m u s e d .$
	Answered by MJS_new last updated on 03/May/21

	$(2 b + 5) (3 b + 2) = b^{3} + b^{2} + 6 b + 3$ $b^{3} - 5 b^{2} - 13 b - 7 = 0$ $(b - 7) {(b + 1)}^{2} = 0$ $\Rightarrow b = 7$
	Commented by ajfour last updated on 03/May/21

	$g r e a t w a y s i r, t h o u g h t o f t h e$ $q u e s t i o n m y s e l f, b u t y o u r$ $m e t h o d i s g r e a t .$
	Commented by MJS_new last updated on 03/May/21

	$we only need to try the natural factors > 1 of$ $the constant of the resulting polynome . if {there}^{'} s$ $no such solution, no base exists$
	Commented by ajfour last updated on 03/May/21

	$i u n d e r s t a n d s i r . .$
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