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2025 VIMC keystage3-IWYMIC individual Question 1

xIMC · 2025 VIMC keystage3-IWYMIC individual

Question 1

An ordered triple of positive integers $(a,b,c)$ is called a V-triple if $a\lt b\lt c$ and it satisfies all the following conditions:
- $a$ is a factor of $b+c$;
- $b$ is a factor of $c+a$;
- $c$ is a factor of $a+b$;
- The sum of $a$, $b$ and $c$ is less than or equal to $2025$.

How many V-triples are there in total?