Solve the following linear congruence, 25x \equiv 15(\bmod 29)

floymdiT 2021-05-09 Answered
Solve the following linear congruence,
\(\displaystyle{25}{x}\equiv{15}{\left({b}\text{mod}{29}\right)}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Tuthornt
Answered 2021-05-11 Author has 23424 answers
Step 1
The given linear congruence equation is
\(\displaystyle{25}{x}\equiv{15}{\left({b}\text{mod}{29}\right)}\)
Here, a=25, b=15, m=29,
And,
gcd(a,m)=gcd(25,29)=1
Hence the congruence has 1 incongruent solution which is given by solving the corresponding Diophantine equation
\(\displaystyle{a}{x}+{b}{y}={m}\Rightarrow{25}{x}+{15}{y}={29}\)
Step 2
Let us check the value of x=11.
That is, at x =11,
\(\displaystyle{11}\times{25}+{15}={275}+{15}={290}\)
which is \(\displaystyle{0}{b}\text{mod}{29}\).
Hence x=11 is the solution of given equation.
Not exactly what you’re looking for?
Ask My Question
24
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...