[PDF] Solutions to Homework Set 3 (Solutions to Homework Problems
2 1 3 If a, b are integers such that a ≡ b (mod p) for every positive prime p, prove that a = b But then by the definition of congruence modulo n a − b = nk for some k ∈ Z But this implies Prove or disprove: If ab = 0 in Zn, then a = 0 or b = 0
[PDF] 3 Congruence
It replaces the con- gruence sign with an equality Theorem 3 3 If a ≡ b mod n then b = a + nq for some integer q, and conversely Proof: If a
[PDF] Congruences - Mathtorontoedu
third number m, then we say "a is congruent to b modulo m", and write a ≡ b ( mod m ) integer k Although some books give this as a lemma or theorem, it is always best to Prove or disprove that if a ≡ b ( mod m ), then a2 ≡ b2 ( mod m)
[PDF] Solutions 31 Prove that if m is an integer, then m 2 ≡ 0(mod 4)
Prove or disprove that if n is odd, then n2 ≡ 1(mod 8) Proof Let n be odd Then there exists an integer k ∈ Z such that n = 2k + 1 Thus we have
[PDF] Number Theory
If a ≡ b (mod m), then a+um ≡ b +vm (mod m) for every integers u and v The assertion of the Fermat' theorem is valid also for some composite numbers
[PDF] Math 346 Final Review Problems Hints and Answers If you find a
So p ≡ kr (mod 30) ⇔ p = kr + 30j for some integer j Then p = k(r + lj) so if k = 1, then k is a factor of p and so p is Prove or Disprove: If a c and b c then ab c
[PDF] Homework 6 - Number Theory Homework
Definition and some basic results and examples The following definition was For example if a ≡ b mod n and b ≡ c mod n, then n (b − a) and n (c − a) We can now do “arithmetic modulo n” by adding and multiplying integers and then
[PDF] Workouts
m for which both i ≡ j (mod m) and k ≡ l (mod m) hold while i k ≡ jl (mod Prove or disprove that: For all integers m and n, if m · n is even, then if n ≡ 1 ( mod p−1) then i n ≡ i (mod Btw This proof needs some care, so please revise your
[PDF] Modular Arithmetic
12 nov 2014 · congruent modulo m, written a ≡ b (mod m), if and only if a – b i e if there is some integer k such that a – b = km If ab and ac, then a(b - c)
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