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Find-the-least-possible-value-of-x-8x-24-mod-16-i-3x-6-mod-25-ii-




Question Number 91732 by I want to learn more last updated on 02/May/20
Find the least possible value of  x      8x ≡ 24 (mod 16)     .... (i)      3x ≡ 6 (mod 25)      .... (ii)
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x} \\ $$$$\:\:\:\:\mathrm{8x}\:\equiv\:\mathrm{24}\:\left(\mathrm{mod}\:\mathrm{16}\right)\:\:\:\:\:….\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\mathrm{3x}\:\equiv\:\mathrm{6}\:\left(\mathrm{mod}\:\mathrm{25}\right)\:\:\:\:\:\:….\:\left(\mathrm{ii}\right) \\ $$
Commented by mr W last updated on 02/May/20
8x=24, 40, 56, ....  ⇒x=3, 5, 7, ....    3x=6, 81,156,...  ⇒x=2,27,52,...    ⇒x_(min) =27
$$\mathrm{8}{x}=\mathrm{24},\:\mathrm{40},\:\mathrm{56},\:…. \\ $$$$\Rightarrow{x}=\mathrm{3},\:\mathrm{5},\:\mathrm{7},\:…. \\ $$$$ \\ $$$$\mathrm{3}{x}=\mathrm{6},\:\mathrm{81},\mathrm{156},… \\ $$$$\Rightarrow{x}=\mathrm{2},\mathrm{27},\mathrm{52},… \\ $$$$ \\ $$$$\Rightarrow{x}_{{min}} =\mathrm{27} \\ $$
Commented by I want to learn more last updated on 02/May/20
Thanks sir
$$\mathrm{Thanks}\:\mathrm{sir} \\ $$

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