Seventeen or Bust Nixes Three Sierpinski Candidates 19
Craigj0 writes "In just 8 days Seventeen or bust has removed three Sierpinski candidates after people have been trying for years. Seventeen or bust is a distributed attack on the Sierpinski problem. You can find the first two press releases here(1) and here(2), the third is still to come. More information about Sierpinski numbers can be found here. Finally they could always use some more people so join!"
Re:How to prove this? (Score:3, Insightful)
8^n - 1 = 7m where for any n m,n are +ve integers
Proof:
the statement is true for n=1 (trivial)
assume it holds for n = some +ve int. k.
8^k - 1 = 7s
Consider the next case:
8^(k+1) - 1
= 8(8^k) - 1
= 8(7s +1) -1
= 56s + 7
= 7(8s+1) clearly divisible by 7.
=>The assertion holds for n=k+1 if it holds for n=k So since n = 1 holds, the assertion holds for all +ve int. n. I'm sure that the techniques these guys use are far more complicated and sophisticated, but it is possible to prove things like that.