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Consider, for a given positive integer \$k\$, the sequence \$(a, a+1, a+2, ..., a+k)\$, where \$a\$ is some positive integer. Is there ever a pair \$a, k\$ such that for each element \$a+i\$ in the sequence, either \$\gcd(a, a+i)\$ or \$\gcd(a+i, a+k)\$ are greater than 1?
This was investigated b...