0
$\begingroup$

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?

$\endgroup$
  • 1
    $\begingroup$ You mean like 99999 in base 10? $\endgroup$ – qwr Dec 18 '18 at 17:30
  • 2
    $\begingroup$ Probably not. They can be written as $b^{k}-1.$ $\endgroup$ – Thomas Andrews Dec 18 '18 at 17:30
1
$\begingroup$

While there is no name, to my knowledge, for the general case, they are referred to as Mersenne numbers for base 2.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.