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Tagged with congruences nt.number-theory
104 questions
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Best way to introduce the Chinese Remainder Theorem (to a high school student)
What do you think to be the most effective way to teach the Chinese remainder theorem to a smart high school student, which is supposed to only have a soft idea about how modular arithmetic works, and ...
CommunityBot
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2
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An elementary question in modular arithmetic
Let us fix a positive natural number $N$. When $i$ is a natural number smaller than $N$, coprime with $N$, we let $\mu(i)$ be the unique number in $\{1, \ldots, N-1\}$ that is the multiplicative ...
CommunityBot
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9
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congruences of level 1 and level p modular forms
I've been carrying out some experiments on the computer and I noticed the following congruence phenomenon: fixing a prime $p$, it seems that any modular form over $SL_2(\mathbb{Z})$ and of weight $k \...
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Solutions to a quadratic congruence
Fix an odd prime $p$. Let $\alpha = (\alpha_0,\dots,\alpha_k)$ be a solution to the congruence $\sum_{i=0}^{k} \alpha_i^2 \equiv x \mod p$. Now consider the number $N_\alpha$ of solutions to the ...
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