In March we posed the problem:
"The number 3723 (in base 10) is written as 123 in another base.
What is that base?" ............ The answer to this can be found in the March problem archive.

We could have written this question as:

Find b where 3723₁₀ = 123_b

So, moving on ...................

123₂₀ is 1 ×20² + 2 ×20 + 3 = 443₁₀

123₂₁ is 1 ×21² + 2 ×21 + 3 = 486₁₀

531 - 486 = 45
486 - 443 = 43

Investigate these differences when 123_b is converted to base 10 (for different values of b).

Try to explain what is happening.