Question

prove that every integer of the form 8^n +1 is acomposite number​

Answer 1

Answer:

Using the J programming language:

Build a function that tests for composite integers:

ct=.1<[:+/"1[:]0<q:

Test it:

ct 1 2 3 4 5 6 7 8 9 10

0 0 0 1 0 1 0 1 1 1 — 1 = composite, 0 = prime

Generate increasing terms of 8^n+1 for n = 0 - 10, and test all terms for composite:

ct 1+8^n=:i.10

0 1 1 1 1 1 1 1 1 1

So all integer terms of 8^n+1 are composite except when n=0

Check up to n=200:

+/ct 1+8^n=:i.200

199

Yes. All terms up to n=200 are composite, except when n=0.

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