Proof: Suppose a ? b mod n. Then by Theorem 3.3 b = a + nq. If a leaves the remainder r when divided by n
Proof: Suppose a ? b mod n. Then by Theorem 3.3 b = a + nq. If a leaves the remainder r when divided by n
If n is an integer then a is congruent to b modulo n if and only if a and b have the same remainder when divided by n. Proof. By the division algorithm
First we notice that if p divides both a and b then p2 divides both a2 Prove that a ? b (mod n if and only if a and b have the same remainder mod n.
Prove that a ? b (mod n) if and only if a and b leave the same remainder when divided by n. Proof. ?. Suppose a ? b (mod n). Then by definition
2 juil. 2010 If a ? c = nk for some integer k then a and c leave the same remainder when divided by n. Remember
Proposition 3. Two integers a b are congruent mod n if and only if they have the same remainder when divided by n. Proof. First
exercises for this chapter asks you to show that if a ? b (mod n) then a and b have the same remainder when divided by n. Page 5. 106. Contrapositive Proof.
Theorem 2. If n ? Zn> 1
18 mar. 2022 Proposition 5. a ? b (mod m) if and only if m
Theorem 3 4If a bmodn then a and b leave the same remainder when divided by n Conversely if a and b leave the same remainder when divided by n then a bmodn Proof: Supposea bmodn Then by Theorem 3 3b=a+nq Ifaleaves the remainder rwhen divided bynwehavea=nQ+rwith 0 r