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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

$$odd+odd=even$$ $$\Rightarrow oddprime+oddprime=even$$ $$$$ $$({prime}_1<{prime}_2)\wedge ({prime}_1+{prime}_2=odd)$$ $$\Rightarrow {prime}_1=2$$ $$\therefore a<p\wedge a+\mathrm{p}=\mathrm{q}\Rightarrow a=2$$

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