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Omni-MATH / Find all the triples of positive integers (a,b,c) for which the number

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Find all the triples of positive integers (a,b,c)(a,b,c) for which the number (a+b)4c+(b+c)4a+(c+a)4b\frac{(a+b)^4}{c}+\frac{(b+c)^4}{a}+\frac{(c+a)^4}{b} is an integer and a+b+ca+b+c is a prime.
Plain-text mathematical notation (without MathML)
Find all the triples of positive integers (a,b,c) for which the number
((a+b)⁴)/(c)+((b+c)⁴)/(a)+((c+a)⁴)/(b)
is an integer and a+b+c is a prime.
Original LaTeX notation
Find all the triples of positive integers $(a,b,c)$ for which the number
\[\frac{(a+b)^4}{c}+\frac{(b+c)^4}{a}+\frac{(c+a)^4}{b}\]
is an integer and $a+b+c$ is a prime.

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Source and history

task_id
0242cc66-7e11-565e-a1f0-0da2e4fe00c3
task_key
test--0242cc66-7e11-565e-a1f0-0da2e4fe00c3
task_revision_id
1
config / split
/ test

Official source

initial import