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Definitions: Here I present a novel conjecture using basic mathematical tools like the sum of the divisors of an integer $n$ called $\sigma(n)$, the sum of the squares of the positive divisors of n ...

As odd squares are congruent to $1$ modulo $8$, any integer of the form $4^k(8m+7)$ with $k,m\in\mathbb N=\{0,1,2,\ldots\}$ cannot be written as the sum of three squares. To avoid such congruence ...