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Old 2020-02-23, 22:17   #1
enzocreti
 
Mar 2018

17·31 Posts
Default Problem...

1763=5879-4423+307


1763 can be written as x-y+z
Where x y z are primes

Are there other primes x y z such that

1763=x-y+z?

Every integer can be written as x-y+z with x y z primes?


Are there others primes x y z such that
1763=x-y+z?

Last fiddled with by enzocreti on 2020-02-23 at 22:21
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Old 2020-02-23, 23:47   #2
Dylan14
 
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"Dylan"
Mar 2017

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An easy way we could do this would be to fix one of the values of x, y and z to a particular prime. For example, let's take z = 53, which is prime.
Then your equation becomes
1763 = x - y + 53, or
1710 = x - y
which implies y = x - 1710. So we merely need to seek solutions where x and x - 1710 are prime. Using the following Mathematica code

Code:
For[x = 1711, x <= 3000, x++, 
 If[PrimeQ[x] && PrimeQ[x - 1710], i++]]
I find 90 such prime values. You can replace the i++ with Print[x, " ", x - 1710, " " , 53] to get the pairs yourself.
I'll leave it to you to generalize this to other z values, or to translate this to a coding language that your machine can handle.

Last fiddled with by Dylan14 on 2020-02-23 at 23:48
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Old 2020-02-24, 00:16   #3
Alberico Lepore
 
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May 2017
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Quote:
Originally Posted by enzocreti View Post

Every integer can be written as x-y+z with x y z primes?
If x, y and z are odd prime numbers

x+z = goldbach

any y

Last fiddled with by Alberico Lepore on 2020-02-24 at 00:31
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