matematicar
New member
- Joined
- Nov 3, 2016
- Messages
- 2
Hello everybody, again I'm stuck in at the middle and don't know how to proceed with the task:
Determine with the proof the set of all prime numbers that can divide two successive integers of the form n^2 + 3.
My work so far (I hope that is correct):
if m is an positive integer then m is divisible by n^2 + 3 and (n+1)^2 + 3
it means that m divides the difference of the terms which is 2n + 1
and
it means that m divides twice the sum of the terms which is (2n+1)^2 + 13
Now I got that m is divisible by 13 (which is a prime number).
But now my struggle is, is that the only prime? Why am I asked for all prime number that can divide two successive integers of the form? Can somebody help me with that part?
Thank you so much!
Determine with the proof the set of all prime numbers that can divide two successive integers of the form n^2 + 3.
My work so far (I hope that is correct):
if m is an positive integer then m is divisible by n^2 + 3 and (n+1)^2 + 3
it means that m divides the difference of the terms which is 2n + 1
and
it means that m divides twice the sum of the terms which is (2n+1)^2 + 13
Now I got that m is divisible by 13 (which is a prime number).
But now my struggle is, is that the only prime? Why am I asked for all prime number that can divide two successive integers of the form? Can somebody help me with that part?
Thank you so much!