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Sums of $M$ consecutive squared integers $\left(a+i\right)^{2}$ equalingsquared integers (for $a\geq1$, $0\leq i\leq M-1$) yield certain lineargroupings of pairs $\left(a_{1},a_{2}\right)$ of $a$ values for successive samevalues of $M$ when these are linked by $a_{1}+a_{2}=\mu M+1$ with$\mu=\left(\eta/\delta\right)\in\mathbb{\mathbb{Q}}^{+}$. In this paper,congruent conditions on $M,\eta,\delta$, and on the difference$\left(a_{2}-a_{1}\right)$ are demonstrated for these linear groupings to hold.It is found that $\eta\equiv1\left(mod\,2\right)$ and $\delta\equiv0,1$ or$5\left(mod\,6\right)$, and if $\delta\equiv0\left(mod\,6\right)$,$M\equiv0\left(mod\,12\right)$, while if $\delta\equiv1$ or$5\left(mod\,6\right)$, $M\equiv2$ or $11\left(mod\,12\right)$ with $a_{1}$ and$a_{2}$ being of different or same parities.

Congruent conditions on the number of terms, on the ratio number of  terms to first terms and on the difference of first terms for sums of  consecutive squared integers equal to squared integers