Generalized way of solving this types of equations x^3+y^4=z^5

Rihanna Bentley

Rihanna Bentley

Answered question

2022-11-10

Generalized way of solving this types of equations x 3 + y 4 = z 5

Answer & Explanation

apopihvj

apopihvj

Beginner2022-11-11Added 20 answers

The equation x 3 + y 4 = z 5 has infinitely many solutions in positive integers. An infinite family of solutions is generated by
x = a ( a 3 + b 4 ) 8 k , y = b ( a 3 + b 4 ) 6 k , z = ( a 3 + b 4 ) 5 k .
There are probably other solutions.
Uriah Molina

Uriah Molina

Beginner2022-11-12Added 7 answers

2 24 + 2 24 = 2 25
( 2 8 ) 3 + ( 2 6 ) 4 = ( 2 5 ) 5
So,
x = 256   ,   y = 64   ,   z = 32

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