let a,b,c be three digits all different of zero Prove that ((ac)/(cb))=(a/b) ⇔ ∀ n≥1 ((accc...cc)/(ccc...ccb)) =(a/b) the number accc...cc has the digit c n times


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Question Number 92188 by ~blr237~ last updated on 05/May/20

$l e t a, b, c b e t h r e e d i g i t s a l l d i f f e r e n t o f z e r o$ $P r o v e t h a t \frac{a c}{c b} = \frac{a}{b} \Leftrightarrow \forall n ⩾ 1 \frac{a c c c . . . c c}{c c c . . . c c b} = \frac{a}{b}$ $t h e n u m b e r a c c c . . . c c h a s t h e d i g i t c n t i m e s$
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