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

Say you're not sure how to start. Say you don't know what the words mean. Say you don't know what the notation means. Say you don't know what the question is asking. Anything. Just don't say "I don't know".In summary, this conversation discusses various mathematical problems involving divisibility and primes. The first problem involves finding the remainder of 15! divided by 17. The second problem states that if (n^2)+2 is prime, then 3 must divide n. The third problem introduces the concept of smallest divisors and states that there exist integers a and b that can be used to show that an+b(p-1)=1. Finally, the fourth problem states that for any n
  • #1
AlexHall
7
0
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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  • #2


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
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?
 
  • #4
TRY one. Make an attempt. Do anything.
 
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Related to Division, Primes, Divisors & Powers: Solve Them All!

1. What is division?

Division is a mathematical operation that involves splitting a number into equal parts. It is the inverse or opposite of multiplication.

2. What are prime numbers?

Prime numbers are numbers that are divisible only by 1 and themselves. They have exactly two factors and cannot be divided evenly by any other number.

3. How do I find the divisors of a number?

The divisors of a number are all the numbers that can evenly divide into that number without leaving a remainder. To find the divisors, you can start by dividing the number by 1 and then checking if there is a remainder. If there is no remainder, then 1 is a divisor. You can then continue dividing by 2, 3, 4, and so on until you reach the number itself.

4. What is the difference between a divisor and a factor?

A divisor is a number that can divide into another number without leaving a remainder, while a factor is a number that, when multiplied by another number, gives the product. For example, in the number 12, the divisors are 1, 2, 3, 4, 6, and 12, while the factors are 1, 2, 3, 4, 6, and 12.

5. What are powers?

Powers, also known as exponents, are a way of representing repeated multiplication. The base number is multiplied by itself a certain number of times, which is indicated by the exponent. For example, 2 to the power of 3 (written as 2³) means 2 multiplied by itself 3 times, resulting in 8 (2 x 2 x 2 = 8).

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