36Here x and y are?
Find all prime numbers that satisfy simultaneously
p+1=2x2
p2+1=2y2
I solved it by the most elementary method can u all do the same
even to prophet Sir(its not a challenge but the simplest solution actually doesnt require number theory)
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4 Answers
1well let me complete the solution
1st we know fo all p x<p
similarly for y y<p
now subtracting the equatins we get
p(p-1)/2=(y+x)(y-x)
now y+x has to be always less than 2p
therefore the value which y+x can be taken is p or 1 it has to p as then y-x will be greater than y+x which is absurd
thereofre y+x=p
y-x=p-1/2
solving we get the value of x and y substitiuting it in the equations we get the only prime solution as 7