Let $(p_i)$ be the sequence of prime numbers. Can we solve the equation:
$$\sum_{i=1}^k p_i^2=\frac{n(n+1)}{2}$$
in $(k,n)$? Note that $(7,36)$ is solution. Is this the unique solution?
Definition 1. An affine plane is a pair $(X,\mathcal L)$ consisting of a set $X$ and a family $\mathcal L$ of subsets of $X$ called lines which satisfy the following axioms:
Any distinct points $x,y\in X$ are contained in a unique line $L\in\mathcal L$;
Any line $L\in \mathcal L$ contains at le...
Let $(p_i)$ be the sequence of prime numbers. Can we solve the equation:
$$\sum_{i=1}^k p_i^2=\frac{n(n+1)}{2}$$
in $(k,n)$? Note that $(7,36)$ is solution. Is this the unique solution?
Definition 1. An affine plane is a pair $(X,\mathcal L)$ consisting of a set $X$ and a family $\mathcal L$ of subsets of $X$ called lines which satisfy the following axioms:
Any distinct points $x,y\in X$ are contained in a unique line $L\in\mathcal L$;
Any line $L\in \mathcal L$ contains at le...
