Questions on the use of Mathematica to find integer/rational solutions to equations.
7
votes
2answers
323 views
Solving/Reducing equations in $\mathbb{Z}/p\mathbb{Z}$
I was trying to find all the numbers $n$ for which $2^n=n\mod 10^k$ using Mathematica.
My first try:
Reduce[2^n == n, n, Modulus -> 100]
However, I receive ...
7
votes
3answers
530 views
Finding the number of solutions to a diophantine equation
I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried:
...
8
votes
2answers
227 views
Is there a way to use functions like Prime[n] within Solve[]?
I'm trying to see if a number can be written as the sum of two prime numbers. Ideally, I would like to use
Solve[Prime[n] + Prime[m] == 100, {n, m}]
But that ...
