Division, Primes, Divisors & Powers: Solve Them All!

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Homework Help Overview

The discussion revolves around various mathematical problems related to division, prime numbers, divisors, and powers. The original poster presents multiple questions, including finding remainders, properties of primes, and divisibility rules.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the first problem involving the remainder of 15! when divided by 17, with hints about using modular arithmetic and Wilson's theorem. The original poster expresses uncertainty about how to approach the remaining problems.

Discussion Status

Some participants have provided hints and encouragement for the original poster to attempt the problems. There is an acknowledgment of the need for effort before receiving assistance, and a suggestion to separate different questions into distinct threads.

Contextual Notes

There is an implied expectation for the original poster to demonstrate some effort in solving the problems, and the discussion reflects a mix of guidance and encouragement to engage with the material more actively.

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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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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Thanks

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

16=-1(mod17)

15!=1mod17

I don't know how to start the other problems. Any tips?
 
TRY one. Make an attempt. Do anything.
 
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