# Repunits whose digits in base $b$ are all $b-1$

Positive integers whose base-$$b$$ representation contains only the digit $$1$$ are called repunits in that base. But what about positive integers whose base-$$b$$ representation contains only the digit $$b-1$$?

For instance, how would one call the base-$$20$$ number whose representation in that base is $$19\cdot19\cdot19\cdot19\cdot19_{20}?$$

Is there a special name for this kind of number? I know repunits are useful in many number-theoretical contexts, but what about such numbers?

• You mean like 99999 in base 10? – qwr Dec 18 '18 at 17:30
• Probably not. They can be written as $b^{k}-1.$ – Thomas Andrews Dec 18 '18 at 17:30