SOLUTION: I need some help understanding modula.
I put -101 mod 3 into a mod calculator and the answer comes up as 3.
Shouldn't it be 2?
-101 / 3 = 33 with 2 remaining.
Or does it change
Algebra.Com
Question 921969: I need some help understanding modula.
I put -101 mod 3 into a mod calculator and the answer comes up as 3.
Shouldn't it be 2?
-101 / 3 = 33 with 2 remaining.
Or does it change somehow with a negative?
Found 2 solutions by rothauserc, Theo:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
You handle the same way you handle positive numbers.
29 ≡ 2 (mod 3)
-101 ≡ -2 (mod 3)
definition of modulus
a congruent b mod m
our example is -101 congruent b mode 3, implies that
-101 -b = 3k for some integer k and therefore -101 -b / 3
-101 -(-2) / 3 = -99 / 3, says that
-101 is congruent to -2 mod 3
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it does change with a negative number but i came up with a different answer than you did.
i got:
101 modulo 3 = 2
-101 modulo 3 = 1
i believe the rule is as follows:
-x modulo y = y - x modulo y
where x >= 0 so that, if x = 5, then -5 is equal to -x.
based on that rule, -101 module 3 is equal to 3 minus 101 module 3 which is equal to 3 minus 2 which is equal to 1.
-101 modulo 3 is not 3 as you stated.
i verified with an online modulo calculator and with excel mod function.
the results of my excel calculations are shown below:
these results confirm the rule is good.
it was difficult to find a reference on the web that didn't confuse me more than i was before i started looking.
after a while i was able to piece it together.
some of the better links i looked at are shown below.
as you will be able to see, there are numerous different methods for how to calculate the modulo of a negative number.
https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/what-is-modular-arithmetic
https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-quotient-remainder-theorem
https://answers.yahoo.com/question/index?qid=20080922034737AAsFEfY
http://www.miniwebtool.com/modulo-calculator/?number1=-340&number2=60
http://mathforum.org/library/drmath/view/52343.html
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