Let be odd primes, integer

If

then

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- Dec 27th 2009, 05:36 AMwauwauproduct of primes II
Let be odd primes, integer

If

then

- Jan 3rd 2010, 02:37 PMabender

(I'll leave this proof to someone else)

So, let's consider the following, seeking contradiction

.

Quite honestly, I'm not sure if this is how you attack this. Fermat's little Thm. applied to sheds light on the fact that

Here we observe that this bit is divisible by 2 (2 consecutive numbers multiplied together), divisible by 3 (one of three consecutive terms certainly is divisible by 3), divisible by 5 (by virtue of the 0(mod 5)), and divisible by 6 since that's 2*3.

Just offering my $0.02. I'd be interested in a elegant solution to this.

-Andy