A Mirror in Every Base

Medium

Call an integer number mirrored in all bases if, written in every base from 2 to number - 2 inclusive, its digits read the same left to right and right to left. Return True if number is mirrored in all bases and False otherwise. Checking every base directly works, but think about whether you can answer without computing anything at all.

Example 1

number=7 → False

In base 2, 7 = 111, a palindrome, but in base 3, 7 = 21, which is not.

Example 2

number=4 → False

Only base 2 needs checking: 4 = 100, not a palindrome.

Constraints

4 ≤ number ≤ 10⁵

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Topics

Brainteaser Math Two Pointers

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Input

number=7

Expected

False

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