Matching a^n b^n c^n for n > 0 with PCRE

How would you match a^n b^n c^n for n > 0 with PCRE?

The following cases should match:

abc
aabbcc
aaabbbccc

The following cases should not match:

abbc
aabbc
aabbbccc

Here's what I've "tried"; /^(a(?1)?b)$/gmx but this matches a^n b^n for n > 0:

ab
aabb
aaabbb

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Note: This question is the same as this one with the change in language.