Hw2 - ,n 4 Find all prime triplets Hint Show that one of the numbers n,n 2,n 4 must be divisible by 3(4 Show that there is no natural number k such

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(1) Consider the binomial expansion ( a + b ) n = C n 0 a n + C n 1 a n - 1 b + ... + C n n b n . Show that C n 0 - C n 1 + C n 2 - ... ± C n n = 0 Hint: Pick appropriate a and b . (2) Find all prime numbers smaller than 100. (3) Recall that prime twins are pairs of prime numbers of the form n,n + 2 such as 3 and 5 or 11 and 13. Similarly, prime ”triplets” are triples of prime numbers of the form n,n + 2
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Unformatted text preview: ,n + 4. Find all prime triplets. Hint: Show that one of the numbers n,n +2 ,n +4 must be divisible by 3. (4) Show that there is no natural number k such that 2 k 1( mod 6). Find all possible values of 2 k ( mod 6). (5) Prove that for any natural k 4 k + 4 9 k 0( mod 5) 1...
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This note was uploaded on 04/26/2011 for the course MATH 246 taught by Professor Applebaugh during the Spring '10 term at University of Toronto- Toronto.

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