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Question Number 152691 by ZiYangLee last updated on 31/Aug/21
If a,p,q are primes with a<p, and  a+p=q, find the value of a.
$$\mathrm{If}\:{a},{p},{q}\:\mathrm{are}\:\mathrm{primes}\:\mathrm{with}\:{a}<{p},\:\mathrm{and} \\ $$$${a}+{p}={q},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}. \\ $$
Answered by Rasheed.Sindhi last updated on 01/Sep/21
odd+odd=even  ⇒odd prime+odd prime=even     (prime_1 <prime_2 ) ∧ (prime_1 +prime_2 =odd)  ⇒prime_1 =2  ∴a<p ∧ a+p=q⇒a=2
$${odd}+{odd}={even} \\ $$$$\Rightarrow{odd}\:{prime}+{odd}\:{prime}={even} \\ $$$$ \\ $$$$\:\left({prime}_{\mathrm{1}} <{prime}_{\mathrm{2}} \right)\:\wedge\:\left({prime}_{\mathrm{1}} +{prime}_{\mathrm{2}} ={odd}\right) \\ $$$$\Rightarrow{prime}_{\mathrm{1}} =\mathrm{2} \\ $$$$\therefore{a}<{p}\:\wedge\:{a}+\mathrm{p}=\mathrm{q}\Rightarrow{a}=\mathrm{2} \\ $$

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