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ZWMath›Elementary number theory›Congruences›Linear congruence›ZW-LINEAR-CONGRUENCE-002
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AreaNumber theoryCourseElementary number theoryTopicCongruences
Divisibility and factorization10
  • Bézout's identity
  • Extended Euclidean algorithm
  • Euclid's lemma
  • Fundamental theorem of arithmetic
  • Least common multiple
  • Infinitude of primes
  • Linear Diophantine equation
  • Greatest common divisor Discrete mathematics
  • Euclidean algorithm Discrete mathematics
  • Prime number Discrete mathematics
Congruences9
  • Complete residue system
  • Modular inverse
  • Linear congruence
  • Chinese remainder theorem
  • Fermat's little theorem
  • Euler's totient function
  • Euler's theorem
  • Wilson's theorem
  • Modular congruence Discrete mathematics
Orders and quadratic residues6
  • Multiplicative order
  • Primitive root
  • Quadratic residue
  • Legendre symbol
  • Euler's criterion
  • Law of quadratic reciprocity
Arithmetic functions5
  • Multiplicative arithmetic function
  • Divisor functions
  • Perfect number
  • Möbius function
  • Möbius inversion formula
Continued fractions and Diophantine equations4
  • Continued fraction
  • Convergent of a continued fraction
  • Pell's equation
  • Sum of two squares
Primes and cryptography3
  • RSA cryptosystem
  • Fermat primality test
  • Prime number theorem

Exercise · ZW-LINEAR-CONGRUENCE-002 · ★☆☆ Basic

What is the greatest common divisor of 4 and 6?

Choose one option.

Show answer
  • B. 2

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Explanation

The common divisors of 4 and 6 are 1 and 2, and the largest is 2, so the greatest common divisor is 2.

Study Elementary number theory in ZWMath →

Review the concept: Linear congruence

A linear congruence is a first-degree congruence in one unknown \(x\), with integer coefficients \(a\), \(b\) and modulus \(m\); its solutions are the integers \(x\) that satisfy it.

\[ax \equiv b \pmod{m}\]

More practice problems: linear congruence

  • ZW-LINEAR-CONGRUENCE-001 What is the modular inverse of 3 modulo 7?
  • ZW-LINEAR-CONGRUENCE-003 How many solutions modulo 10 does the congruence 3x ≡ 1 pmod10 have?
  • ZW-LINEAR-CONGRUENCE-004 Does the congruence 2x ≡ 1 pmod4 have a solution?
  • ZW-LINEAR-CONGRUENCE-005 What is the value of x in x ≡ 3 pmod5 that lies between 0 and 4?
  • ZW-LINEAR-CONGRUENCE-006 Solve 3x ≡ 2 pmod7. What is the solution modulo 7?
  • ZW-LINEAR-CONGRUENCE-007 Solve 5x ≡ 4 pmod9. What is the solution modulo 9?
  • ZW-LINEAR-CONGRUENCE-008 Solve 2x ≡ 4 pmod6. How many solutions modulo 6 does it have?
  • ZW-LINEAR-CONGRUENCE-009 Solve 4x ≡ 2 pmod10. What is the set of solutions modulo 10?

← ZW-LINEAR-CONGRUENCE-001 ZW-LINEAR-CONGRUENCE-003 →

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