Reducing Numbers: Can Big Numbers be Simplified?

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In summary, the conversation is discussing the possibility of reducing any number to the form x^n + y, where n is not equal to 1 and y is either +1 or -1. The person has tried multiple numbers and has not found a contradiction to these rules yet. They also mention another possible form, x^n + y where -x+1 < y < x-1, but it is not clear if this is possible. The conversation also touches on the condition n>1 and how it relates to the previous forms. The person asks for further explanation in simpler terms.
  • #1
ziad1985
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There is something going through my mind recently.
is it possible to reduce any number to the following form:
x^n +y , and -x+1<y<x-1?? x isn't necessarily prime
or better something like this x^n +y where y=+1 or -1
I tried many numbers, so far I can't see a contradiction to these 2 rules I stated, or maybe there is one, but can't really see it.
I want to see if it's possible to reduce a very very big number, to a simpler form, like the 2 i stated above.
example:(I don't know if this is correct)
1...million zero...1
it should be reduced to this 1000^1000 +1
 
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  • #2
One assume you do not consider n=1 acceptable.

If not then you obviously can't have the extra condition that y=+/-1, as not every number is one more or less than a perfect power.
 
  • #3
what about the first way I thought of ?
x^n +y , and -x+1<y<x-1 not possible too ?
 
  • #4
Again, you're assuming n>1, obviosuly, but not bothering to state it. And again it is trivial to show it is possible if you relax it to less than or equal in the condition with y. And always with n=2. What are the two extremes? x(x-1) and x(x+1).

I leave it to you to finish that proof, and to think what it implies for your other question with a strict inequality.
 
  • #5
Can you explain what you are saying in some other way, I maybe be good in English, but along with mathematics they don't really mix together for me..
 
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Related to Reducing Numbers: Can Big Numbers be Simplified?

1. How can big numbers be simplified?

Big numbers can be simplified by breaking them down into smaller factors. This process is known as prime factorization. It involves finding the prime numbers that can be multiplied together to get the original number.

2. Why is it important to reduce big numbers?

Reducing big numbers can make them easier to work with and understand. It can also help with calculations and comparisons. Additionally, it can reveal patterns and relationships between numbers.

3. Can all big numbers be simplified?

No, not all big numbers can be simplified. Some numbers, known as prime numbers, can only be divided by 1 and itself. These numbers cannot be further reduced.

4. Are there any tricks for simplifying big numbers?

Yes, there are some tricks that can make simplifying big numbers easier. These include looking for common factors, using divisibility rules, and using a calculator or computer program.

5. How is reducing big numbers useful in real life?

Reducing big numbers is useful in many real-life situations, such as budgeting, cooking, and understanding statistics. It can also be helpful in solving problems in fields like finance, engineering, and computer science.

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