Primes and certain unit fractions Are there primes p , q and a natural number a

Banguizb 2022-07-07 Answered
Primes and certain unit fractions
Are there primes p , q and a natural number a such that 1 p + 1 q = 1 a ?
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Answers (1)

Janiyah Patton
Answered 2022-07-08 Author has 12 answers
Only for p = q = 2. Indeed, if it is the case, then
p + q p q = 1 a
and p + q divides p q. But only 1, p, q and p q divide p q. Certainly p + q is not any of the three first numbers. The other possibility is
p + q = p q
But in this case,
( p 1 ) ( q 1 ) = p q p q + 1 = 1
Therefore, p = q = 2

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