## a mod 5 = 2 and b mod 5 = 3 what is ab mod 5?

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
hbelle
Posts: 9
Joined: Fri May 28, 2010 1:52 am

### a mod 5 = 2 and b mod 5 = 3 what is ab mod 5?

If a and b are integers and a mod 5 = 2 and b mod 5 = 3, what is ab mod 5?

Am I on the right track? I'm starting with n = dq + r and solving for a & b first:
a = c5 + 2
b = d5 + 3 so,
(c5 + 2)(d5 + 3) mod 5 = solution
(25cd +15c + 10d + 6) mod 5 = solution
we know that 25cd +15c + 10d divides evenlyl by 5 so we just look at the remaining 6, 6 mod 5 = 1

so is ab mod 5 = 1?

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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### Re: a mod 5 = 2 and b mod 5 = 3 what is ab mod 5?

If a and b are integers and a mod 5 = 2 and b mod 5 = 3, what is ab mod 5?

Am I on the right track? I'm starting with n = dq + r and solving for a & b first:
a = c5 + 2
b = d5 + 3 so,
(c5 + 2)(d5 + 3) mod 5 = solution
(25cd +15c + 10d + 6) mod 5 = solution
we know that 25cd +15c + 10d divides evenlyl by 5 so we just look at the remaining 6, 6 mod 5 = 1

so is ab mod 5 = 1?
yes