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Source. Definition 5.1 and Theorem 2, printed p. 1746, physical PDF p. 8.

Convention

A covering system

$$C=\{r_i\pmod{m_i}\}_{i=1}^t$$

is an $(a,b)$-primitive $m$-covering if it is an $m$-covering and there are distinct primes $p_1,\ldots,p_t$ such that $p_i$ is a primitive prime divisor of $a^{m_i}-b^{m_i}$ for every $i$.

Statement

"Let $a$ and $b$ be relatively prime positive integers. If $a+b$ is not a power of 2, then there exists an $(a,b)$-primitive 3-covering." (p. 1746)

Proof pointer. The proof on printed pp. 1746--1747 uses the paper's explicit covering, Zsigmondy's theorem, and a separate replacement of the modulus-$6$ class in the case $(a,b)=(2,1)$. It was not reconstructed or independently checked here.