Question

- this proof is true or false ? than is false so why and where ?

Answer 1

- let p and k prims ,p,k > 2 , the form of p=2a+1 and k=2b+1 ,where a and b are natural numbers
from N
- and let n >= 2 ,n natural number from N
- prove that for every n will be a number a and a number b such that the equation n=a+b+1 is
true
- so if p=2a+1 than a=(p-1)/2 and so if k=2b+1 than b=(k-1)/2
- so than n=a+b+1
- so n=(p-1)/2 +(k-1)/2 +1
- for n=2 than 2=(2-1)/2 +(2-1)/2 +1 so 2=1/2 +1/2 +1 so 2=1+1 so 2=2
- for n=3 than 3=(3-1)/2 +(3-1)/2 +1 so 3=1+1+1 so 3=3
- for n than n=(2a+1-1)/2 +(2b+1-1)/2 +1 so n=2a/2 +2b/2 +1 so n=a+b+1
- for n=k so than k=a+b+1 suppose is true
- so than for k=k+1 will be k+1=(2a+1-1)/2 +(2b+1-1)/2 +1 +1 so k+1=2a/2 +2b/2 +1 +1 so
k+1=a+b+1+1 so k+1=k+1

Answer 2

dear ,,lalaly" please you ansqer me !!! thank you very much

Answer 3

answer

Answer 4

I don't understand this step:

- for n=2 than 2=(2-1)/2 +(2-1)/2 +1 so 2=1/2 +1/2 +1 so 2=1+1 so 2=2

Why can insert 2 for p and k?

Answer 5

how do you think please ? this induction proof is

Answer 6

so p and k are prims

Answer 7

What happens at that step?

Answer 8

p and k can beeing indifferent prims just need satisfied this conditions for what when n=2 the right part resulted 2 too

Answer 9

so this proof by complete induction is true or false ?

Answer 10

Oh, I see, You want to show it's true for n=3 and so you choose p and k equal to 3.

Answer 11

yes but indifferent when so for every values of n there will be one value for p and one value for k when this statement is true

Answer 12

so this statement i thought that can beeing proven by complete induction

Answer 13

So, in the final step you need to show that you can write k+1 as k+1=a+b+1.

But I don't see that in your proof?

Answer 14

With a and b not necessarily the same as for k.

Answer 15

but there is k+1=(a+b+1) +1

Answer 16

on the last lines

Answer 17

But a and b needs to come from prime numbers. If there was no restriction for a and b you could just take a= n-1 and b=0, so you n=n-1+1

So you need to show that 2a+1 and 2b+1 is prime.

Answer 18

but these was on substitution added,wrote on the first lines

Answer 19

You need to show that k+1=x+y+1, with x,y natural numbers >=2 and 2x+1, 2y+1 prime.

You've shown that k+1=a+b+1+1. So now first you need to get to the form k+1=x+y+1. for example you can do k+1= a + (b+1)+1. Then for this example you need to show that 2a+1 is prime and 2(b+1)+1 is prime.

Answer 20

Also, are you trying to prove the statement, or just find out if the proof is good?

Answer 21

so 2a+1 is prime sure
and 2(b+1)+1 =2b+2+1 =2b+3 can being prime too for b=1,2,4,5,...

Answer 22

2a+1 is prime sure because we know that every primes are in the form of 2a+1

Answer 23

True,

Also, I'm not saying using (b+1) was a good idea. It might work, it might not.

Answer 24

so for this have you some differents ideas ?

Answer 25

Not right now, no.

Answer 26

Are you sure the statement is true? It's quite hard to prove something that's not true, and I've never seen this statement before.

Answer 27

yes is true
please check these examples from the first lines

Answer 28

It's not true for n=2:

n=a+b+1=2
a+b=1
a and b are natural numbers so either one of them is zero, let's say a=0.
p=2*0+1=1, but 1 isn't prime.

Answer 29

2=(2-1)/2 +(2-1)/2 +1
2=1/2 +1/2 +1
2=1+1
2=2 so is true

Answer 30

and is right because 2 is prime

Answer 31

and yes this is one specialy case because 2 not can be writing in the form of 2a+1

Answer 32

but 1/2 is not a natural number. I assume that's necessary.

Answer 33

As I've said earlier, if there are no restrictions for a and b it's simple.

Answer 34

not is necessary check it please on substitution bacause there are wrote that the first example is case specially

Answer 35

and a and b are from the form of primes

Answer 36

where a and b are natural numbers sure

Answer 37

how do you think now after these specifications this proof can be considered true or false ?

Answer 38

I think it's false/incomplete, because you haven't shown that k+1 can be written as x+y+1 with 2x+1 and 2y+1 prime.

Answer 39

from p=2x+1 --- x=(p-1)/2 and t=2y+1 --- y=(t-1)/2
so than k+1=(p-1)/2 +(t-1)/2 +1 where we us for these two primes p and t for we can differentes from the k what we us in our proof

Answer 40

Can you say that again, I didn't understand that sentence...

Answer 41

so yes initialy there i have used like primes p and k ,yes ? ... so but because in the math induction proof we us n=k and after this n=k+1 so for this i have said in my last lines that we need using different sign ,and not k ,so for this we can using for second prime saying t so t=2b+1 so b=(t-1)/2
ok ?

Answer 42

so n=a+b+1
n=(p-1)/2 +(t-1)/2 +1
when n=2 than there are n=(2-1)/2 +(2-1)/2 +1
so 2= 1/2 + 1/2 +1
so 2=1+1
so 2=2
- this was a specialy case
- so when n=3 than 3=(3-1)/2 +(3-1)/2 +1
so 3=1+1+1 so 3=3
- for n=4 than will be 4=(5-1)/2 +(3-1)/2 +1
so 4=2+1+1 so 4=4
........
than suppose that for n=k is true and we need to prove that is true for n=k+1

Answer 43

so for n=k will be k=(p-1)/2 +(t-1)/2 +1 so k=(2a+1 -1)/2 +(2b+1-1)/2 +1 so
k=2a/2 +2b/2 +1 so k=a+b+1 so than this we suppose that is true and now we need to prove that for k=k+1 will be true too
- so for k=k+1 than k+1=a+b+1+1 so k+1 =(2a+1-1)/2 +(2b+1-1)/2 +1+1 so
k+1=2a/2 +2b/2 +2 so k+1=a+b+1+1 but because a+b+1=k so than we get
k+1=k+1
- what is your opinion please from this now ?