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

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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