calculatorcryptographymodular arithmetic
I'm wondering does anyone know of a scientific calculator with a mod function?
In C# this is shown as follows (just in case there are any other mods that a mathematical non-savant such as myself wouldn't be aware of)
5 % 4 = 1
I've looked through the most common ones on the web but the function is either not in the list or not present.
I have a little bit of a bias towards Casio calculators as that's what I'm familiar with but will accept any suggestions that can be currently purchased.
Derek
Let's use successive squaring:
\begin{align*} 18^2 = 324 \equiv 49 &\equiv -6 \pmod{55} \\ 18^4 \equiv (-6)^2 &\equiv 36 \pmod{55} \\ 18^8 \equiv 36^2 \equiv 1296 &\equiv 31 \pmod{55} \\ 18^{16} \equiv 31^2 \equiv 961 &\equiv 26 \pmod{55} \end{align*}
Now we have
$$18^{17} = 18^{16 + 1} = 18^{16} \cdot 18 \equiv 26 \cdot 18 \equiv 28 \pmod{55}$$
This approach never necessitates using numbers larger than $55^2 = 3025$, and can be done by hand easily. In fact, by allowing negative results in our computations, we can only deal with numbers between about $-30$ and $30$, which is even easier.
Going swiftly through the calculators's Manual I found this section which explains the only use of the $X\ \& \ Y$ buttons:
Hence the confirmation of what you suspected: this calculator does not solve any equations
Best Answer
Virtually every graphing calculator made in the recent past has a mod function. Many scientific calculators do as well, though the documentation is often lacking.