# Modulo Arithmetic

• Mar 4th 2009, 07:53 AM
boomshine57th
Modulo Arithmetic
Hey guys. Could somebody help me please?

i was ill the day the lecture on modulo was on and lecture notes dont make sence to me :(

a) find a number in Z/7 which gives 1 mod 7 when multiplied by 3

b) use the answer to (a) to solve the equation 3n=4 in Z/7

thank you guys!

Best Regards
• Mar 4th 2009, 09:18 AM
GaloisTheory1
Quote:

Originally Posted by boomshine57th
Hey guys. Could somebody help me please?

i was ill the day the lecture on modulo was on and lecture notes dont make sence to me :(

a) find a number in Z/7 which gives 1 mod 7 when multiplied by 3

b) use the answer to (a) to solve the equation 3n=4 in Z/7

thank you guys!

Best Regards

a. $5$ b/c $5 \cdot 3=1 \in Z/7.$
b. similar to part a.
• Mar 4th 2009, 11:47 AM
HallsofIvy
Quote:

Originally Posted by boomshine57th
Hey guys. Could somebody help me please?

i was ill the day the lecture on modulo was on and lecture notes dont make sence to me :(

a) find a number in Z/7 which gives 1 mod 7 when multiplied by 3

To coin a phrase, "just DO it". What is 3*1 (mod 7)? What is 3*2 (mod 7)? What is 3*3 (mod 7)? What is 3*4 (mod 7)? What is 3*5 (mod 7)? ?What is 3*6 (mod 7)?

Quote:

b) use the answer to (a) to solve the equation 3n=4 in Z/7
I don't see how the answer to (a) helps to solve that equation but the [b]method does: while you were calculating those, which was congruent to 4 (mod 7)?

Quote:

thank you guys!

Best Regards