If-a-p-q-are-primes-with-a-lt-p-and-a-p-q-find-the-value-of-a-

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 .

Answered by Rasheed.Sindhi last updated on 01/Sep/21

o d d + o d d = e v e n

\Rightarrow o d d p r i m e + o d d p r i m e = e v e n

({p r i m e}_{1} < {p r i m e}_{2}) \land ({p r i m e}_{1} + {p r i m e}_{2} = o d d)

\Rightarrow {p r i m e}_{1} = 2

∴ a < p \land a + p = q \Rightarrow a = 2