n= -67. and n=43

AIMEBOY wrote: n= -67. and n=43 Yup! It Would be great if you could post your solution as well

parmenides51 wrote: Find all integers$ n$ such that $n^2 + 24n + 35$ is a square. Let $n^2 + 24n + 35$ = $x^2 eqn.1$ $n^2 + 24n + 35 + 109$ = $x^2+109$ $(n+12)^2$= $x^2 +109$ $(n+12)^2-x^2$=109 $(n+12+x)(n+12-x)$ = 109 Since Rhs is a prime no. Therefore $(n+12-x) = 1$ $(n+12+x)=109$ On simplifying we'll get x=54, substituting it in eqn 1, we get $n^2 +24n - 2881 =0$ The solutions to this quadratic are the only soln,i.e. 43,-67

MathX322 wrote: AIMEBOY wrote: n= -67. and n=43 Yup! It Would be great if you could post your solution as well Given above