Key to "Primes and certain unit fractions Are there primes..."

Banguizb

Answered question

2022-07-07

Primes and certain unit fractions
Are there primes

p, q

and a natural number

a

such that

\frac{1}{p} + \frac{1}{q} = \frac{1}{a}

Janiyah Patton

Beginner2022-07-08Added 12 answers

Only for

p = q = 2

. Indeed, if it is the case, then

\frac{p + q}{p q} = \frac{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

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?