Help Needed: Prime, Square & 0s - Seeking Direction

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In summary, Gokul is trying to find the highest power of 2 in 1100, but can't seem to find a pattern. Matt is trying to solve for the p that is what he is looking for.
  • #1
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hello all. i am in dire need of direction here and i really appreciate all this help.

how many 0's are in 1100!

prove tuv=(tu,tv,uv)[t,u,v]

only prime that makes 4p+1 a perfect square is p=2.

can anyone please help me? i am in so much need of direction... :confused: :cry:
 
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  • #2
for the one about highest common factors, this time I would in the first instance just prove it using prime decomposition, though that is not the most admirable way.

suppose 4p+1=x**2, rearrange and factorize and use the defining properties of primes in Z: a number, q, is prime iff when ever q|ab then q|a or q|b.

Remember, this is just mathematics, things just follow from the definitions, sometimes by a clever trick but not usually in questions like this.

Yes there is still soem work for you to do here, but you need to indicate how you're trying to solve them, so start with these hints and tell us how far you get.
 
  • #3
1. What contributes a '0' to the decimal representation of a product of numbers ? Think about 5s and 2s. Also think about what is the highest power,k, of a prime number, p < n, such that p^k divides n! Try some examples and you'll find a pattern...
 
  • #4
:smile: woooo, it is by these people on this great site that is making me understand this theory stuff! God love you all! :smile:
 
  • #5
Gokul43201 said:
1. What contributes a '0' to the decimal representation of a product of numbers ? Think about 5s and 2s. Also think about what is the highest power,k, of a prime number, p < n, such that p^k divides n! Try some examples and you'll find a pattern...
perhaps there are 189 zeros?
 
  • #6
matt, by setting it up like this, do i solve for the p b/c that is what i am looking for right? do i'd have 4p+1=x**2. = 4p=x^2-1 and then divide by 4, thus, p=x^2-1/4. pick an x and show that it is prime? reply and let me nkow if this is right.

i'm sorry gokul, i just cannot find a pattern here yet... i can see how i.e. p=11 but that is all i can come up with.. I'm sorry if I'm not seeing it yet plese maybe a little more insight??
 
  • #7
Please don't divide like that. Use divisibilty. Since 4p=(x+1)(x-1) and prime factorizations are unique in Z then one of the following cases must hold: x+1 is one of 1,2,4,p,2p or 4p, and x-1 the other factor. Which of those systems gives of equations is solvable in Z with p prime?
 
  • #8
How many multiples of 5 among [1,1100] ? Clearly, this is = floor(1100/5) = 220.

But then, every multiple of 25 gives you and extra factor of 5 not counted above. There are floor(1100/25)=44 such 5s.

Similarly there are floor(1100/125) = 8 additional factors of 5 from multiples of 125.

And finally, there is 625, which gives you another extra 5.

So the higest power of 5 in 1100! is 220+44+8+1=273 {which is just = floor(1100/5) + floor(1100/5^2) + floor(1100/5^3) + floor (1100/5^4) }

Similarly, you can find the highest power of 2 in 1100! The lower of these two numbers gives you the highest power of 10 in 1100!, which is the number of zeros.
 
  • #9
Loop Quantum Gravity,

One of us is wrong. I think I'm right.
 

FAQ: Help Needed: Prime, Square & 0s - Seeking Direction

What is the purpose of the "Help Needed: Prime, Square & 0s - Seeking Direction" project?

The purpose of this project is to identify and analyze patterns in a given set of numbers, specifically prime numbers, square numbers, and 0s. This can help us gain a better understanding of number patterns and potentially make predictions about future number sequences.

How can I contribute to this project?

There are a few ways you can contribute to this project. You can help by suggesting new ideas or approaches for analyzing the numbers, providing feedback on the current methods being used, or by actively participating in the data collection and analysis process.

What is the significance of studying prime numbers and square numbers?

Prime numbers and square numbers have been studied for centuries and hold a great deal of importance in mathematics. These numbers have unique properties and patterns that have helped us understand the nature of numbers and their relationships. Additionally, prime numbers have practical applications in fields such as cryptography.

Can this project be applied to other types of numbers?

Yes, this project can be applied to other types of numbers such as triangular numbers, Fibonacci numbers, or even real-world data sets. The methods and techniques used in this project can be adapted to analyze different types of numbers and patterns.

How can the findings from this project be used in real-world applications?

The findings from this project can be used to make predictions about number sequences, which can have practical applications in fields such as finance, statistics, and computer science. Additionally, the methods used in this project can be applied to other data sets to gain insights and make predictions.

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