Prime Numbers

For students of class 9-10 (age 14-16)
Naheed
Posts:20
Joined:Sun Dec 16, 2012 11:10 pm
Prime Numbers

Unread post by Naheed » Thu Jan 28, 2016 12:22 pm

For $n\in \mathbb N$, find the values of $n$, so that $3n-4, 4n-3$ and $5n-3$ can be prime numbers.
Last edited by Phlembac Adib Hasan on Sun Aug 07, 2016 1:35 pm, edited 1 time in total.
Reason: Latexed

tanmoy
Posts:312
Joined:Fri Oct 18, 2013 11:56 pm
Location:Rangpur,Bangladesh

Re: Prime Numbers

Unread post by tanmoy » Thu Jan 28, 2016 2:05 pm

$3n-4+4n-3+5n-3=12n-10$.So,at least one of them is even.The only even prime is $2$.Only $3n-4$ and $5n-3$ can be even.Solving the equatios $3n-4=2$ and $5n-3=2$,we get that $n=2$ and $n=1$.Only $n=2$ makes all the three given numbers prime.So,$n=2$ is the only solution.
"Questions we can't answer are far better than answers we can't question"

Naheed
Posts:20
Joined:Sun Dec 16, 2012 11:10 pm

Re: Prime Numbers

Unread post by Naheed » Fri Jan 29, 2016 1:07 am

Nice! Thanks.

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