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The equation isn't prime...

It's in the form of a^2-b^2

IT CANNOT BE PRIME!

It is the factors of (a-b) x (a+b).

Whatever...

Factoring the equation, we get the following factors:

(2 ^ 1024) - 1=(2^512 - 1) x (2^512 + 1)

Now you may see something that you can do. 

Factor.

We can factor this equation for a long time until you get:

(2 - 1) x (2 + 1) .

Yay!

CONGRATS :)

Just do the Pythag. Theorm. I can't tell you the answer since you didn't show any work. I can show you if you show some work.

Do you really need help with this? 

Alright...

We can draw a square around the triangle, then take out parts of it to make the shaded triangle.

The square around it has an area of 16. (4x4=16)

The three triangles we take out of the square to get the shaded triangle have an area of:

2, 4.5, and 2

Add them up to find 8.5

16-8.5 is 7.5

I think it's relatively simple...

Yay!

@ElectricPavlov, When n=106 is the 375th locker, it is the 375. So, 375. My new answer is 67/94. I think that's right.

I don't know why it won't let me type the question. Let me reformat it

Point P is on side AC of triangle ABC such that angle APB = angle ABP, and angle ABC - angle ACB = 39 degrees.

Find angle PBC in degrees.

Sorry. Here is the full question:

Point P is on side AC of triangle ABC such that

Find

But, at least I showed my work :)

should be the second one, i believe.

The inverse function is \(f^{-1}(x) = \dfrac{-5x - 1}{2x + 1}\), so a/c = -5/2.

Thank you!

I'm sure there's a more clever way than this. Anyways:

We write the prime factorization of 30! to get 2^26×3^14×5^7×7^4×11^2×13^2×17×19×23×29 (using Wolfram Alpha). The prime factors here are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. So there are 10 prime divisors of 30!.

Truncated pyramid        also    frustum of a pyramid

okay, theres your reasoning, EP, lol:)

Well... it has to be an odd number because when divided by 2  there is a remainder

it has to be a multiple of 5   + 4         so I started at  9    then 14   then 19   until I got a 'system' in mind....and thought 59 was the answer....  it works....I didn't check all of the lower numbers that were   multiples of 5  +4

Oh yah....I GUESS (in an educated way, I suppose) on answers sometimes...particularly probability questions....then I usually enclose an    '(I think) '   !          I DO NOT know all of the answers....sometimes I 'try'....which is just slightly better than 'guessing'      HaHa

First drop  405  meters    then it goes up AND down      2/3 (405)  =  270     

second bounce   goes up and down         2/3 270 = 180

third bounce     up and down     2/3  180 =   120

405   + 2 (270)  + 2(180 )   + 2(120) = ........m

123456. Ones digit must end in 2, 4 or 6. That is 3 choices x 5!(5 x 4 x 3 x 2  x 1) = 360 numbers.