Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

#26 2014-06-12 22:20:33

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

I like to post on how to be a better problem solver. From my point of view this is way more important than being good at math. Many math types are not good problem solvers. Instructing a student in calculus or number theory is a job for the school system. But since you are asking I will give you what I have about mods and congruences if you have the time.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#27 2014-06-12 22:23:40

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

Yes I have the time. I want to be a better problem solver, but I can't solve a problem when I don't have the maths required to solve it. Like brittle math 2 for example, I have to know about v = d/t but I can solve Brittle Math 1 because no maths is required.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#28 2014-06-12 22:28:02

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

The mod operator returns the remainder when one number is divided by another.

For instance:

5 mod 3 is 2 because when 5 is divided by 3 there is a remainder of 2.

37 mod 9 is 1 because when 37 is divided by 9 there is a remainder of 1.

8 mod 2 is 0 because when 8 is divided by 2 there is a remainder of 0.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#29 2014-06-12 22:31:18

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

nvm got it. I saw 85 just now

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#30 2014-06-12 22:32:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

Okay, you do a few:

123 mod 11 is ?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#31 2014-06-12 22:38:50

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

2

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#32 2014-06-12 22:45:40

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

That is correct. What is

5^3 mod 10 ?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#33 2014-06-12 22:46:27

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

5

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#34 2014-06-12 22:47:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

What is 6^4 mod 100 ?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#35 2014-06-12 22:50:00

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

96

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#36 2014-06-12 22:52:11

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

That is correct. What is 10^19 mod 10 ?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#37 2014-06-12 22:53:53

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

0

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#38 2014-06-12 22:56:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

That is correct. We write mods in this way.

When we say 13 mod 2 = 1 we write that as

this is read as 13 is congruent to 1 mod 2.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#39 2014-06-12 22:58:03

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

I got that

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#40 2014-06-12 23:02:44

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

123 mod 11 = 2 is written

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#41 2014-06-12 23:04:23

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

I got that too

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#42 2014-06-12 23:05:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

Okay then what does this say

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#43 2014-06-12 23:07:05

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

100 is congruent to 0 mod 10

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#44 2014-06-12 23:07:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

In ordinary words what does it mean?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#45 2014-06-12 23:17:51

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

100 is same to mod 10

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#46 2014-06-12 23:19:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

Not quite, it means 100 leaves a remainder of 0 when divided by 10. This is another way of saying 10 divides 100.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#47 2014-06-12 23:24:08

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

Oh

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#48 2014-06-12 23:25:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

Did you notice that taking mod 10 of any number gets the last digit?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#49 2014-06-12 23:28:11

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,137

Re: Find the unit digit of the number n

Yes

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

Offline

#50 2014-06-12 23:29:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Find the unit digit of the number n

So taking the mod 10 of this

should get the last digit.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline