# Question 17

Number Theory Level 5

How many positive integral pairs $$(a,b)$$ can make the below expression true? $(a,b)+9[a,b]+9(a+b)=7ab$

• Notes:

1.$$(a,b)$$ stands for the GCD (Greatest common divisor) of integers $$a$$ and $$b$$;

2.$$[a,b]$$ stands for the LCM (Lowest common multiple) of integers $$a$$ and $$b$$.

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