twisted_logic89
New member
- Joined
- Oct 20, 2008
- Messages
- 23
Definition: If a,b,n are integers we say that a is congruent to b (mod n) if and only if n divides (a - b)
Show that if a is congruent to b (mod n) and c is a whole number then ac is congruent to bc (mod n)
Show that if a is congruent to b (mod n) and c is congruent to d (mod n) the a + c is congruent to b + d (mod n)
Show that if a is congruent to b (mod n) and c is congruent to d (mod n) then ac is congruent to bd (mod n)
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alright... on the first one, a is congruent to b (mod n) can be rewritten as: a - b = nr
if c is a whole number then ac is congruent to bc........ I am not sure how to prove this....
2nd problem: a is congruent to b (mod n) = a - b = nr
c is congruent to d (mod n) = c - d = nq
if I add the two, it would be (a - b) + (b - c) = a -c = nr + nk
I don't understand how this shows that a + c is congruent to b + d....
3rd problem: same stuff as problem number two but ....... I was told to solve for a, solve for c, then multiply those two together....... how do I solve for them?
Show that if a is congruent to b (mod n) and c is a whole number then ac is congruent to bc (mod n)
Show that if a is congruent to b (mod n) and c is congruent to d (mod n) the a + c is congruent to b + d (mod n)
Show that if a is congruent to b (mod n) and c is congruent to d (mod n) then ac is congruent to bd (mod n)
----
alright... on the first one, a is congruent to b (mod n) can be rewritten as: a - b = nr
if c is a whole number then ac is congruent to bc........ I am not sure how to prove this....
2nd problem: a is congruent to b (mod n) = a - b = nr
c is congruent to d (mod n) = c - d = nq
if I add the two, it would be (a - b) + (b - c) = a -c = nr + nk
I don't understand how this shows that a + c is congruent to b + d....
3rd problem: same stuff as problem number two but ....... I was told to solve for a, solve for c, then multiply those two together....... how do I solve for them?
