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-

Tinku Tara June 4, 2023 Integration 0 Comments

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

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

$${let}\:{a},{b},{c}\:{be}\:{three}\:{digits}\:{all}\:{different}\:{of}\:{zero} \\ $$$${Prove}\:{that}\:\frac{{ac}}{{cb}}=\frac{{a}}{{b}}\:\Leftrightarrow\:\forall\:{n}\geqslant\mathrm{1}\:\:\:\:\frac{{accc}…{cc}}{{ccc}…{ccb}}\:=\frac{{a}}{{b}}\:\:\: \\ $$$${the}\:{number}\:{accc}…{cc}\:\:\:{has}\:{the}\:{digit}\:{c}\:\:{n}\:{times} \\ $$

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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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