Life can be so easy ... or not to see the wood for the trees

Written by Ines

Thursday, 14 May 2009 12:03

It is embarrassing. I've spent nearly an hour for proving that if $n \geq 7$ then 7 divides $n!$ . Well, I tried several proof methods but I was very certain that Proof by Induction is the correct one. After a while, I washed the dishes to distract me from thinking (my husband will be happy, because it was his turn today ;) ), I returned to my desk and googled, but nothing.

Then I just wrote down $6! = 1 \times 2 \times 3 \times 4 \times 5 \times 6$ and $7! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7$ and asked myself what is the difference between $6!$ and $7!$ and suddenly it was clear. Of course, a number which includes the factor 7 is divisible by 7.

Life can be so easy. :)

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