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Question-202170




Question Number 202170 by sonukgindia last updated on 22/Dec/23
Answered by AST last updated on 22/Dec/23
112=a2^m ⇒a2^(m−4) =7⇒2^(m−4) =1⇒m=4;a=7  11392=b2^n =2^7 ×89⇒n=7;b=89  (7+89)≡8(mod 4+7);⇒(a+b)≡8(mod (m+n))
$$\mathrm{112}={a}\mathrm{2}^{{m}} \Rightarrow{a}\mathrm{2}^{{m}−\mathrm{4}} =\mathrm{7}\Rightarrow\mathrm{2}^{{m}−\mathrm{4}} =\mathrm{1}\Rightarrow{m}=\mathrm{4};{a}=\mathrm{7} \\ $$$$\mathrm{11392}={b}\mathrm{2}^{{n}} =\mathrm{2}^{\mathrm{7}} ×\mathrm{89}\Rightarrow{n}=\mathrm{7};{b}=\mathrm{89} \\ $$$$\left(\mathrm{7}+\mathrm{89}\right)\equiv\mathrm{8}\left({mod}\:\mathrm{4}+\mathrm{7}\right);\Rightarrow\left({a}+{b}\right)\equiv\mathrm{8}\left({mod}\:\left({m}+{n}\right)\right) \\ $$

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