Question

Show that there is no prime number p for which 2p+1 is a square number.

Answer 1

HI!!

Answer 2

if you have an odd square, do you know what it is modulo 4?

Answer 3

If p is prime then p is odd except for 2.
\[
a^2\equiv1\pmod 4\\
2p+1\equiv 1\pmod 4\\
2p\equiv 0 \pmod 4
\]
Implying p is even? For p=2, 2p+1 = 5 so it is impossible for 2p+1 to be square?

Answer 4

done

Answer 5

That looks neat !