# Tagged Questions

Modular arithmetic (clock arithmetic) is a system of integer arithmetic based on the congruence relation $a \equiv b \pmod{n}$ which means that $n$ divides $b-a$.

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### Hypothetical equation (modulo a power of two) and the value [duplicate]

We have hypothetical equation: $2^{b} \% k = z$. Assume that we know $z$, $b$ and $k$. So everything! We want to know only if the above equation is true. I do not want to use the exponentiation ...
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### How to find remainder when $975^{40153}$ is divided by $14$? [duplicate]

I still find tricky this kind of problems. I tried to do solve it by factoring $14$ in $2*7$. Then, with Fermat's Little Theorem, I find that: $975^6\equiv 1\pmod 7$ $975^1\equiv 1\pmod 2$ How can ...
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### What is (a mod n) mod n?

I have an equation such as (a + b) mod n which is nothing but (a mod n + b mod n) mod n according to this. Now, I know that b mod n is 0 which results in (a mod n) mod n. Is this equivalent to a ...
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### Solving Modular Equation

Let $d$ and $n$ be coprime. What is the smallest positive solution for x in the equation: $$d^x \equiv 1 \mod n$$ This value must depend on both $d$ and $n$. We know that the maximum value for it is ...