List questions from modular-arithmetic

46

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Prove for non prime $n$ there exists $m \in \mathbb{Z}/n\mathbb{Z} \setminus \{0\}: m^{n-1} \neq 1 \mod n$

Published on 25 Mar 2026 - 4:42

170

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Prove that there exist infintely many primes $p$ with $p\equiv2$ or $-2 \pmod{5}$

Published on 25 Mar 2026 - 0:27

43

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Arithmetic of integers, divisibility

Published on 24 Mar 2026 - 23:43

417

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Identity involving binomial coefficients

Published on 25 Mar 2026 - 4:35

82

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Use Euler's Criterion to deduce that $5^{2^{2^{n}-1}}\equiv -1 \space \text{mod} \space p $

Published on 05 Feb 2018 - 22:08

245

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Understanding quadratic reciprocity

Published on 22 Mar 2026 - 20:47

131

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Is "$a^p + b^p = c^p + d^p \Rightarrow (a+b) \equiv (c+d) \mod p$" true?

Published on 21 Mar 2026 - 23:09

157

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Fermat's Last Theorem And Modular Arithmetic

Published on 25 Mar 2026 - 1:15

564

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Raising an expression involving modulo operator to a power.

Published on 20 Mar 2026 - 19:31

73

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Compute 189 × 214 (mod 15) by reducing first, then multiplying, then reducing again

Published on 17 Mar 2026 - 4:15

1.3k

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Discuss the solution to 5x ≡ 8(mod 10)

Published on 17 Mar 2026 - 15:38

2.4k

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Proof: If a ≡ b (mod n) then am ≡ bm (mod mn) and converse

Published on 17 Mar 2026 - 15:04

5.1k

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Find all solutions to $x^2$ ≡ 1(mod 8)

Published on 20 Mar 2026 - 8:45

37

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Number of solutions for quadratic polynomials in $\mathbb{F}_p$

Published on 22 Mar 2026 - 19:41

295

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Conclude there are infinitely primes with given residue class

Published on 20 Mar 2026 - 16:45

List Question

Prove for non prime $n$ there exists $m \in \mathbb{Z}/n\mathbb{Z} \setminus \{0\}: m^{n-1} \neq 1 \mod n$

Prove that there exist infintely many primes $p$ with $p\equiv2$ or $-2 \pmod{5}$

Arithmetic of integers, divisibility

Identity involving binomial coefficients

Use Euler's Criterion to deduce that $5^{2^{2^{n}-1}}\equiv -1 \space \text{mod} \space p $

Understanding quadratic reciprocity

Is "$a^p + b^p = c^p + d^p \Rightarrow (a+b) \equiv (c+d) \mod p$" true?

Fermat's Last Theorem And Modular Arithmetic

Raising an expression involving modulo operator to a power.

Compute 189 × 214 (mod 15) by reducing first, then multiplying, then reducing again

Discuss the solution to 5x ≡ 8(mod 10)

Proof: If a ≡ b (mod n) then am ≡ bm (mod mn) and converse

Find all solutions to $x^2$ ≡ 1(mod 8)

Number of solutions for quadratic polynomials in $\mathbb{F}_p$

Conclude there are infinitely primes with given residue class

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