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Find all $x \in \mathbb Z_{360}$ such that $x^2 ≡ 0 \pmod{360}$

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#elementary-number-theory #modular-arithmetic #prime-factorization
76
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Calculate the sum $ \sum\limits_{i=1}^n \sum\limits_{j=1}^n a_i \mod a_j $ in $\mathbb{Z}.$

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#summation #modular-arithmetic
1.4k
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inverse matrix with modulo

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#matrices #modular-arithmetic #gaussian-elimination
749
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Prove by Induction if x is an odd integer, then for every integer n ≥ 0, $x^{2^n}$ ≡ 1 (mod $2^{n + 1}$)

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#elementary-number-theory #proof-writing #modular-arithmetic #divisibility
52
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Construction of sequence satisfying some bound

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#sequences-and-series #number-theory #modular-arithmetic
223
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Last digits of iterated triangular numbers

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#modular-arithmetic
427
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Lattice vectors and modular arithmetic

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#number-theory #elementary-number-theory #modular-arithmetic #integers #integer-lattices
129
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Suppose $\bar{a}\in (\mathbb{Z}/n\mathbb{Z})$*. Prove that $\gcd(\bar{ab},n)=\gcd(\bar{b},n)\forall_{b\in (\mathbb{Z}/n\mathbb{Z})}$

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#group-theory #modular-arithmetic #divisibility #gcd-and-lcm
100
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What does this notation mean in modular arithmetic?

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#notation #modular-arithmetic
76
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What is the dual ring of Z/pZ?

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#ring-theory #modular-arithmetic
84
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expression with inverses in modular equation

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#modular-arithmetic #arithmetic
98
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Does $x$ always exist?

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#elementary-number-theory #modular-arithmetic
1k
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Why $5 (\mod 7)$ is $5$?

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#modular-arithmetic
181
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Hard Modulo arithmetic

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#modular-arithmetic #congruences
91
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Prove that $\Bbb Z/6\Bbb Z\cong\Bbb Z/3\Bbb Z \times\Bbb Z/2\Bbb Z$

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#abstract-algebra #group-theory #modular-arithmetic #gcd-and-lcm

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