If 2n+1 is a perfect square,then n+1 is the sum.of two perfect squares.

[@piotrskalski1477]

2n+1=:k^2 k must be odd, because its square is. n+1=k^2/2 +1/2 from adding 1 then dividing the last eq. by 2 k=:2j+1. n+1=(4j^2+4j+1)/2 +1/2 n+1=2j^2 + 2j +1 n+1=j^2 + (j+1)^2

[@Auroiniumgaming]

ejsy+

[@Archimedes_Notes]

@@piotrskalski1477 1/2 does not belong to n. We do not define that in N, the set of natural numbers.

[@piotrskalski1477]

@@Archimedes_Notes I divided by 2. Two halfs gave a one, I don't see a problem

[@anonymousmuffin956]

@@Archimedes_Notes just because two numbers are not in N does not mean we only have to work with numbers in N. 1/2 + 1/2 is a member of N even though it consists of rational numbers, so there is no problem here. Even though -1 is not a natural number, we can still do n + -1, which would give a natural number for n > 1 with similar reasoning.

[@Archimedes_Notes]

@@anonymousmuffin956 what i mean is that when we solve in N we do not tre