Does 625!625! have 156156 zeros at the end?

Someone wrote that 625!‘s last 156 digits are zeros because 125+25+5+1=156. If it’s true that 625! has 156 zeros at the end, how does “125+25+5+1=156” prove it? Answer When you factorize 625!, you are interested in the number of 10s you can divide it by until it is no longer possible to divide evenly. But … Read more

Do theories and proofs in decimal mathematics work in other numeral systems? Is there a field of mathematics which deals with this question?

The mathematics we use today is based on the decimal system. I was wondering if some or all of these proofs would hold true in other numeral systems. For example binary or hexadecimal. Is there any field which works with questions like this? Answer With rare exception, mathematics works with numbers, not numerals, so the … Read more

What is the name for number systems beyond hexadecimal? [closed]

Closed. This question does not meet Mathematics Stack Exchange guidelines. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for Mathematics Stack Exchange. Closed 2 years ago. Improve this question I know the name of the first couple base n number systems. But what comes after that? … Read more

How do you convert $(12.0251)_6$ into fractions?

How do you convert $(12.0251)_6$ (in base 6) into fractions? I know how to convert a fraction into base $x$ by constantly multiplying the fraction by $x$ and simplifying, but I’m not sure how to go the other way? Answer I assume you want decimal notation in your fraction. We have $$(12.0251)_6=(1\times 6^1) + (2\times … Read more

Solving simultaneous equations with imaginary numbers

Consider the following simultaneous equation: {5z−(3+i)w=7−i(2−i)z+2iw=−1+i What is the simplest way to manipulate one of the equations so that a variable can be eliminated and the equation solved? Answer You do it the same way you do it over the reals. For example, you could solve the first equation for z, z=(7−i+(3+i)w)/5, substitute that into … Read more

Why does casting out 99 and 1111 work to compute remainders?

I found two examples that I’d like to understand: Example 1: Find 112358132134 \mod 9. Solution is: 1+1+2+3+5+8+1+3+2+1+3+4 \mod 9 = 7 \mod 9 = 7 Example 2: Find 62831853 \mod 11. Solution is: (-6)+2+(-8)+3+(-1)+8+(-5)+3 \mod 11 = -4 \mod 11 = 7 My question is: Based on what property we sum the digits of … Read more