# Twice a square

Number Theory Level 5

Find a positive integer $$N$$ such that $$p^3 + N^2$$ is a perfect square for 2 distinct (positive) primes $$p$$.

Details and assumptions

You may use a theorem of Ljunggren, which states that the equation $$x^2+x+1=y^3$$ has only the following integer solutions: $$(x,y)=(0,1), (−1,1), (18,7), (−19,7)$$.

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