Problem #321

Consecutive Zeros Mobius
Public 04/08/16 8xp Math 14.9%


It can easily be seen that there cannot be more than 3 consecutive integers such as $ \mu(n_i) = \pm 1,\quad\mu(n) $ being the Möbius function

However, we can find arbitrary long sequences of consecutive integers with a Möbius value of 0.

Find 9 consecutive integers $ n+1,n+2, ..., n+9 \textrm{ such as }\mu(n+i) = 0$
(Each of them is divisible by a distinct prime square, the primes are the smallest possible).

Answer format: n

[My timing: 10 sec]



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