Claims

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1970_10_01_golomb: Golomb's observation that 12167 = 23^3 and 12168 = 2^3 3^2 13^2 are consecutive powerful numbers with neither a square, answering the first question no; refereed in the American Mathematical Monthly.

1976_04_01_walker: Walker's 1976 theorem that the equation 7^3 x^2 = 3^3 y^2 + 1 has infinitely many solutions, each giving two consecutive powerful numbers with neither a square; refereed in the Fibonacci Quarterly.

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