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How to solve congruence system

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#modular-arithmetic #systems-of-equations
179
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Find integer $n$ modulo composite.

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#combinatorics #number-theory #prime-numbers #modular-arithmetic
32
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prove that $[5, 7, 11, 13, 17, 19, 23]$ are the only possible variants of the remainders (read context) when dividing the prime number $p$ by 24

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#prime-numbers #modular-arithmetic #divisibility
2.8k
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Get all linear congruences of $3x\equiv 6(mod9)$

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#number-theory #modular-arithmetic
1.1k
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Solve $x\equiv 1\pmod{5}, x\equiv 2\pmod{6}, x\equiv 3\pmod{7}$

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#modular-arithmetic #chinese-remainder-theorem
52
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Solve $x\equiv 1\bmod2, x \equiv 1\bmod5$ and $x \equiv 0\bmod3$

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#number-theory #modular-arithmetic #chinese-remainder-theorem
1k
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Solve $x\equiv 1\pmod2$, $x\equiv 2\pmod3$, $x\equiv 3\pmod4$, $x\equiv 4\pmod5$, $x\equiv 5\pmod6$ and $x\equiv 0\pmod7$

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#number-theory #modular-arithmetic #chinese-remainder-theorem
46
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Runtime of modular expansion

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#modular-arithmetic #cryptography
597
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How does one prove that $n^2 +5n + 16$ is not divisible by $169$ for any integer $n$?

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#elementary-number-theory #discrete-mathematics #modular-arithmetic #divisibility
127
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The proof of $(n+1)!(n+2)!$ divides $(2n+2)!$ for any positive integer $n$

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#discrete-mathematics #modular-arithmetic #factorial #prime-factorization #ceiling-and-floor-functions
187
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If I have n+1 element, why is it true that there will always be at least two that are congruent, modulo n?

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#modular-arithmetic #pigeonhole-principle
65
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How to solve this modulo equation using modulo properties?

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#elementary-number-theory #modular-arithmetic
37
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Inverting exponentiation modulo a prime

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#modular-arithmetic
47
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Which of $[0]_3, [1]_3, [2]_3$ is $[5^k]_3$ equal to?

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#modular-arithmetic
1.2k
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Find all solutions in modular arithmetic

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#abstract-algebra #discrete-mathematics #modular-arithmetic

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