Two squares

Got me ?
There are so many others who are far far...(infinite times) better than me...

hehe , good one soumik.

now that we have got u also here, we can start killing the maths ones

2) Since 2n+1 represents a square 2n+1=4s+1, meaning n is even, hence 3n+1=6s+1, thus x is odd. Using the fact that when a and b are odd, 8|a^2-b^2, we have 8|n… 2n+1 is actually congruent to 1,9,5 modulo 10, meaning n has to be congruent to 0,4,2,9,7 modulo 10 Checking for each, we have that n congruent to 0 (mod10) is the only possibility… Thu 5|n, meaning 40|n.

this had been dicussed in goiit already
i jus saw that thread there

but MTG is not all the source of all plympiads. real olympiads are those which need us to find the answer `NOT CHOOSE IT`

i dont know how to start with sir can u give me ne clues

check by putting option given in the exam [4]

oops ok

2nd part is not as easy as the 1st part

at the end of solution some manual calc needs to be done also for certain values

2nd part is quite good to think off.

so any juniors up to it?

(celestine i request u not to give any hint please)

let 2n+1=k² and 3n+1=m²

then 5n+3= (2k)²-m² =(2k+m)(2k-m)

so obviously 5n+3 is not a prime

hey manipal u need to prove n=40 X ()..

clue

5n+3 = 4(2n+1) - (3n+1)

203 is divisible by 7 also