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Prime Numbers
Posted: Thu Jan 28, 2016 12:22 pm
by Naheed
For $n\in \mathbb N$, find the values of $n$, so that $3n-4, 4n-3$ and $5n-3$ can be prime numbers.
Re: Prime Numbers
Posted: Thu Jan 28, 2016 2:05 pm
by tanmoy
$3n-4+4n-3+5n-3=12n-10$.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.
Re: Prime Numbers
Posted: Fri Jan 29, 2016 1:07 am
by Naheed
Nice! Thanks.