Find the smallest positive integer solution to the following system of congruence: xequiv 17(mod 35) xequiv 8(mod 43)

bobbie71G 2021-02-23 Answered
Find the smallest positive integer solution to the following system of congruence:
x17(mod 35)
x8(mod 43)
You can still ask an expert for help

Want to know more about Congruence?

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

Brighton
Answered 2021-02-24 Author has 103 answers
Now x=17+35k, for some kZ
Then,
17+35k8(mod 43)
35k9(mod 43)
35k34(mod 43)
gcd(35,43)=1
Then, there exists x,y \in Z such that
35x+43y=1
35=4×8+3
43=35×1+8
8=3×2+2
3=2×1+1
1=32×1
1=3(83×2)×1
1=3×38×1
1=3×(354×8)8×1
1=3×358×13
1=3×35(4335×1)×13
1=16×3543×13
1=35(16)+43(13)
Hence,x=16
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

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