0

Given a natural number n, and two integers a and b. Show that if:

a)a ≡ b and b≡c, it follows that a≡c

b)a≡b and c≡d, it follows that a+c≡b+d and ac≡bd

c)that a≡b if and only if a and b give the same remainder when divided by n

*I solved a) by equating k_1n with k_2n (there k_1n=a-b and k_2n = b-c). Although I am not sure how to continue with examples b) and c)...

Bill Dubuque
  • 265,059
  • 37
  • 279
  • 908
Aristarchus_
  • 347
  • 1
  • 1
  • 9
  • 1
    Please show your work. For more information about the MathSE protocol on posting questions, see [this article](https://math.meta.stackexchange.com/questions/33190/how-to-avoid-downvotes-for-beginners-questions/33236#33236). – user2661923 Jul 13 '22 at 17:06
  • For (b) see the congruence sum & product rules in the first dupe, and for (c) see the 2nd dupe. – Bill Dubuque Jul 13 '22 at 17:16
  • In (b) $a -b = kn$, $c-d = mn$ so $a+c-(b+d) = (k+m)n$. – Rishi Jul 13 '22 at 17:25

0 Answers0