abac-dc-2-d-ab-c-c-2-ac-abac-

Question Number 215272 by Rasheed.Sindhi last updated on 02/Jan/25

{\begin{cases} \overset{―}{a b a c} = {(\overset{―}{d c})}^{2} \\ d = \frac{\overset{―}{a b}}{c} \\ c^{2} = \overset{―}{a c} \end{cases}

\overset{―}{a b a c} = ?

Answered by A5T last updated on 02/Jan/25

c^{2} = \overset{―}{ac} \Rightarrow c = 0, 1, 5 or 6; d = \frac{\overset{―}{ab}}{c} \Rightarrow c \neq 0

c = 1 \Rightarrow a = 0 \Rightarrow d = b

\Rightarrow 100 b + 1 = {(10 d + 1)}^{2} \Rightarrow 100 b + 1 = {100 b}^{2} + 1 + 20 b

\Rightarrow {100 b}^{2} - 80 b = 0 \Rightarrow b = 0 \Rightarrow d = 0

a = b = d = 0; c = 1 \Rightarrow \overset{―}{abac} = 0001

c = 5 \Rightarrow a = 2 \Rightarrow 5 d = 20 + b \Rightarrow (d, b) = (4, 0); (5, 5)

Checking \Rightarrow (d, b) = (4, 0) \Rightarrow \overset{―}{abac} = 2025

c = 6 \Rightarrow a = 3 \Rightarrow 6 d = 30 + b \Rightarrow (d, b) = (5, 0), (6, 6)

Checking \Rightarrow None works

\Rightarrow \overset{―}{abac} = 2025 or 0001

Commented by Rasheed.Sindhi last updated on 02/Jan/25

H a p p y 2025 s i r!

T h a n k s f o r n i c e a n s w e r!

Commented by A5T last updated on 02/Jan/25

Same to you, thanks .

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