Number Theory

  • Thread starter AlexHall
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  • #1
AlexHall
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1) Find the remainder of the division of 15! with 17

2) If (n^2)+2 prime show that 3 divides n

3)If p the smallest divisor for n show that there exist integers a and b such that an+b(p-1)=1

4) For every n>1 show that n does not divide (2^n)-1

Any help?
 
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Answers and Replies

  • #2
Dick
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You really have to show some kind of effort (even if it's unsuccessful) before people can help. And break different questions up into different threads. But I'll give you a free hint for the first one. The integers mod 17 are a group under multiplication. Or just use Wilson's theorem. So what is 16! mod 17?
 
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  • #3
AlexHall
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Thanks

16!=-1(mod17)
16!=15!.16=-1(mod17)

16=-1(mod17)

15!=1mod17

I dont know how to start the other problems. Any tips?
 
  • #4
Dick
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TRY one. Make an attempt. Do anything.
 
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