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