1. Diophantine equations

1. Are there integers x and y so valid: $\displaystyle x^2 -5xy +y^2 =3$ ?
2. Are there prime p and natural n so: $\displaystyle 3p+1=k^3$ ?
3. Determine the naural numbers: $\displaystyle 2<a<b<c<d<e$ so: $\displaystyle \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+ \frac{1}{d}+ \frac{1}{e} = 1$.