All Answers 357307 Answers

87
75, 68, 61, 54, 47, 40, 33, 26
63                           28
51                           16                  
39, 32,  25, 18, 11,  4

The rule is -12 as a common difference for "down"

The rule is -7 as a common difference for "across"

0+1+2+3+4+5+6+7 =28 base 10

28/8 =3 + 4 as a remainder

so, the answer is 34 base 8.

ant101 what is the answer then?

Incorrect, tertre. we know it has to be 5 and up.

No, that's incorrect.

We can set up variables: 7x=5964, 12x=5964/7*12=10224 total votes.

Hmm, I give a take at this.

Okay, thank you!

This is old, but...

(Derived from AoPS' Alcumus, thank you!)

You are very welcome!

:P

Is this supposed to have a pic with it?

Hi Rom,

Thanks, but I hope you do not think it was a request from me.

This question has NOT captured my imagination.

I was just trying to make the asker and other answerers think a little more.

If you are looking at it because it interests you personally then I appologise for butting in :)

Yes, I guess so.  Thanks Chris. 

Don't you know the words 'thank you'!

It was very nice of guest to go to this trouble for you !

You can spoon feed babies but sometimes they are still not happy.

Are you sure of your equation?   Is it   + 5   at the end....or should it be  (x+5)  multiplier?

Read your question! What do n and m stand for?

No votes are   7 out of 12     yes votes are  5 out of 12

7/12 = 5964 votes

total votes =    5964  * 12/7  = 10224  total votes

$5(2a-5+b)$

I'll give you a hint.

$\text{since }f(z) \text{ has the stated property }\forall z\\ f(1) \text{ is equidistant from }(0,0i), \text{ and }(1,0i)\\ \text{The locus of these points is }\left(\dfrac 1 2 , i y\right),~\forall y \in \mathbb{R}\\ \text{From this you can figure out }a\\ \text{Once you have }a \text{ finding }b \text{ is trivial}$

2.

7(4-x)=2(y-3)    ⇒  28 - 7x = 2y - 6 ⇒  2y + 7x  =  34    (1)

4(x-y)=7-y ⇒  4x - 4y = 7 - y  ⇒  3y - 4x = - 7      (2)

Multiply (1) by 3   and (2) by -2

6y + 21x  = 102

-6y + 8x   =   14             add these

29x = 116         divide both sides by 29

x = 4

And using  (1) to find y

2y + 7(4) = 34

2y + 28 = 34

2y = 6

y = 3

So   (x, y)  =  (4, 3)

1. 2(x+y)=y+10

    4(x+y)=5y+32 

Simplify

2x + 2y  = y + 10   ⇒   2x  +  y  =  10  ⇒ y = 10 - 2x    (1)

4x + 4y = 5y + 32 ⇒    4x - y  = 32    (2)

Sub (1)  into (2)  for y

4x - (10 - 2x) = 32

6x - 10   = 32

6x = 42

x  = 7

And using (1)    y = 10 - 2(7)  =  -4

So   (x, y)  =  (7, -4)

$\text{Using Euler's Theorem}\\ 17^{\varphi(102)}\equiv 1 \pmod{102}\\ \varphi(102) = 32\\ 1507 = 32 \cdot 47 + 3\\ 17^{1507} = 17^{32 \cdot 47 + 3} = 17^{32\cdot 47}17^3 \equiv 17^3 \pmod{102}\\ \text{this we can solve by brute force w/o too much trouble}\\ 17^3 = 4913 = 48\cdot 102 + 17 \equiv 17 \pmod{ 102}$

I think something like this has more of a number theory type solution.

Chinese remainder theorem or something.

I will tinker with it and see if anything pops out.

thank you !

please help 

The last answer is correct....