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Find the remainder when $13^{13}$ is divided by $25$.

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#modular-arithmetic
178
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Euclidean GCD calculation and mod

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#number-theory #modular-arithmetic #gcd-and-lcm
80
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Prove that $x$ is congruent to $y \pmod m$ if and only if $x = km + y$

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#elementary-number-theory #modular-arithmetic
338
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Solve quadratic congruence equation by completing square

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#number-theory #modular-arithmetic #quadratics
721
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Find the smallest positive integer $X$ such that $478^{870} \equiv X \ (\text{mod} \ 273)$

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#modular-arithmetic
551
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Simultaneous congruence with a coefficient for x

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#modular-arithmetic
1.7k
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How to prove "Unit digit of a square number"?

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#number-theory #elementary-number-theory #modular-arithmetic #quadratic-residues
73
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Congruences implied by division.

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#number-theory #modular-arithmetic
349
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Analogous results to Euler's theorem

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#number-theory #modular-arithmetic
1.6k
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Exhibit a reduced residue system mod 7 composed entirely of powers of 3

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#elementary-number-theory #modular-arithmetic
65
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Is this a correct mathematical statement about integers mod n and congruence mod n?

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#modular-arithmetic #proof-explanation #solution-verification #equivalence-relations
1.5k
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Prove $x^4 +x+1$ is irreducible in $\mathbb{Z}/2\mathbb{Z}[x]$

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#modular-arithmetic #irreducible-polynomials #polynomial-rings
407
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How to solve $(x \mod 7) - (x \mod 8) = 5$?

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#modular-arithmetic
71
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Linear Congruences in One Variable.

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#modular-arithmetic
92
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Solve $x^n \equiv -1 \ (mod \ p)$ given $n$ and prime $p$

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#number-theory #algorithms #modular-arithmetic

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