Let $5\leq p_1<\cdots<p_r$ be primes, put $P=p_1\cdots p_r$, and let $g_P(2n)$ count the unordered decompositions $2n=h+k$ for which both summands are coprime to $6P$. We derive an explicit finite inclusion--exclusion formula for $g_P(2n)$ by parametrizing the admissible residue classes and combining the local restrict...
Let p ≥ 5 be prime, and let g(2n, p) denote the number of unordered representations
by positive integers
2n = h + k, h ≤ k, gcd(h, 6p) = gcd(k, 6p) = 1.
Every positive integer coprime to 6 belongs to exactly one of the families 6z + 1 and
6z + 5. In each family, divisibility by p excludes one explicit residue class of...
Andres Salazar· Communications on Number The...· 1 citation
Let $p_1,\dots,p_r\geq 5$ be distinct primes, let $P=p_1\cdots p_r$, and put $M=6P$. For a positive integer $n$, let $g_P(2n)$ denote the number of unordered representations $2n=h+k$, with $1\leq h\leq k$, such that $\gcd(h,M)=\gcd(k,M)=1$. Using the canonical remainder operator $\delta_q(x)=x-q\lfloor x/q\rfloor$, we...
Andres M. Salazar· 0 citations
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