Hey willy0625.
I vaguely remember results regarding 1 (mod 4) and 3 (mod 4) for prime-ness and composite numbers. Maybe you could search for those results and see if they apply in your situation.
This Olympiad questions states:
[Show that every term of the sequence 10001, 100010001, 1000100010001, ... is composite.]
Well, I figured out this sequence is generalised as a_{n} = 10001^{n} for all n 1.
After actually doing this division in Excel(I know... I cheated), I found out the prime factorisation of 10001 = 73*137, hence proving the claim.
If I had no access to Excel, how would you have come up with this factorisation. Any results we can make use of to get the prime factorisation?
Thanks
Hello, willy0625!
Show that every term of the sequence 10001, 100010001, 1000100010001, ... is composite.
Well, I figured out this sequence is generalised as a_{n} = 10001^{n} for all n 1. . No!
Not true . . .. . . . . . Note the "binomial" pattern.
Want to try it again?