Problem 44849. Given a base n, find the y values less or equal than 100(without 1), such that they will never produce a periodic number if we divide any whole number between some of them

A periodic number depends on the base b where we are working. So, for example the number 2/3 in decimal base is periodic(0.666666666) but if we are working in base 3, the same number can be expressed as 2/10, and the result is not periodic (0.2). By this way, it is possible to enunciate:

• In base 2 or 3, all numbers will produce periodics numbers unless the number is the base or power of the base
• In decimal base, numbers as 2,5,8,40,50 for example will never produce periodics numbers.

By this way, you have to find when a number in any base can produce periodics numbers or not, and then find the values less or equal than 100 that in this base will never produce a periodic number.