Prime or Composite?

Number Theory Level 3

Let n n be a positive integer such that 2 n + 1 2n + 1 and 3 n + 1 3n +1 are both perfect squares. Then 5 n + 3 5n + 3 is?

1 Composite number I can't solve this problem. Prime number

Mihir Chakravarti by mihir Chakravarti , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Meet Patel
Apr 3, 2019

Let 2 n + 1 = p 2 2n+1=p^2 and 3 n + 1 = q 2 3n+1=q^2 Now, 5 n + 3 = 4 ( 2 n + 1 ) − 3 n + 1 = 4 p 2 − q 2 = ( 2 p − q ) ( 2 p + q ) 5n+3= 4(2n+1)-3n+1= 4p^2-q^2=(2p-q)(2p+q)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...