Prime numbers
Lê Anh Duy
31/12/2018 at 05:05
# ¤ PUBG ¤ # 18/01/2019 at 09:49
If x = 2 , we have x2 + 2x = 8 ( scrap because 8 isn't a prime number)
If x = 3 , we have x2 + 2x = 17 ( satisfy )
If x > 3 and x is a prime number then x =3k + 1 or 3k + 2 ( k is a natural number)
+) x = 3k +1
If x = 3k +1 then x2 divide to 3 has the remainder 1
and 2x divide to 3 has the remainder 2
=> 2x + x2 divided to 3
But 2x + x2 > 3
So 2x + x2 isn't a prime number
Do the similar to x = 3k+2
The answer is x = 3

Nguyễn Mạnh Hùng 09/01/2019 at 13:09
If x = 2 , we have x^{2 }+ 2^{x} = 8 ( scrap because 8 isn't a prime number)
If x = 3 , we have x^{2} + 2^{x }= 17 ( satisfy )
If x > 3 and x is a prime number then x =3k + 1 or 3k + 2 ( k is a natural number)
+) x = 3k +1
If x = 3k +1 then x^{2 }divide to 3 has the remainder 1
and 2^{x} divide to 3 has the remainder 2
=> 2^{x }+ x^{2 }divided to 3
But 2^{x }+ x^{2 }> 3
So 2^{x }+ x^{2} isn't a prime number
Do the similar to x = 3k+2
The answer is x = 3

Conandtb 11 hour ago (14:25)
If x = 2 , we have x2 + 2x = 8 ( scrap because 8 isn't a prime number)
If x = 3 , we have x2 + 2x = 17 ( satisfy )
If x > 3 and x is a prime number then x =3k + 1 or 3k + 2 ( k is a natural number)
+) x = 3k +1
If x = 3k +1 then x2 divide to 3 has the remainder 1
and 2x divide to 3 has the remainder 2
=> 2x + x2 divided to 3
But 2x + x2 > 3
So 2x + x2 isn't a prime number
Do the similar to x = 3k+2
The answer is x = 3
Lê Anh Duy
25/07/2018 at 15:18
Tôn Thất Khắc Trịnh 26/07/2018 at 01:26
I'm going to assume that a,b and c can coincide with eachother.
Selected by MathYouLike
So a=3, b=1, c=3
a=c=3;
\(\overline {ab}\)=\(\overline {cb}\)=31;
\(\overline {abc}\)=\(\overline {cba}\)=313;
Of which all are prime.
It feels cheating to do it this, but you have to get the smallest prime so... oh well