Claims

../

1984_06_01_heath_brown: Heath-Brown proves that tau(n) equals tau(n plus 1) for infinitely many n, at least a constant times x over the seventh power of log x of them up to x, answering the question of Erdős and Mirsky affirmatively.

1987_10_01_hildebrand: Hildebrand proves that tau(n) equals tau(n plus 1) for at least a constant times x over (log log x) cubed integers n up to x, answering the question again with a far larger count.

1997_12_01_pinner: Pinner proves that for every positive integer B there are infinitely many n with tau(n) equal to tau(n plus B), which at B equal to one answers the question again.

---