Unformatted text preview: (iii) Find gcd(819 , 165) using the Euclidean algorithm. 5. Find integers x , y such that 819 x + 165 y = 3 . 6. There are inﬁnitely many primes. 7. 4 √ 8 is irrational. 8. For every real number b , there is a natural number n ∈ N such that b < n . HINT: Assume by way of contradiction that the result is false. Then apply LUB to the set N . 9. Suppose a , b ∈ N and a,b ≥ 1. Then gcd( a,b )lcm( a,b ) = ab. HINT: Use Theorem 3.27. 1...
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 Spring '08
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 Natural number, Prime number, Euclidean algorithm, prime factorizations

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