Positive integer solutions to \frac{1}{a}+\frac{1}{b} = \frac{c}{d}\,,, where c and d

Jaidyn Cook

Jaidyn Cook

Answered question

2022-04-25

Positive integer solutions to 1a+1b=cd,,,
where c and d are positive integers such that gcd(c,d)=1.

Answer & Explanation

Felicity Carter

Felicity Carter

Beginner2022-04-26Added 16 answers

Step 1
1a+1b=cd,,
Above has solution:
a=(3k2)
b=(k2)(3k2)
c=(k1)(3k2)
d=(k2)(3k2)2
Step 2
For k=5 we get:
(a,b,c,d)=(13,39,52,507)

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