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Exercise 1: Find 20 consecutive composite numbers.
Exercise 2: Prove that for any positive integers m and n the following
relation holds:
mn = gcd(m,n) . lcm(m,n).
Exercise 3: Prove that there are infinitely many primes.
Exercise 4: Let a and b be two relatively prime (coprime) numbers. Prove
that if c is an integer such that a|c and b|c then ab|c.
Exercise 5: Prove that for positive integers m and n, there exists integers x
and y suchthat mx + ny = gcd(m,n).

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Week 1

  • 1. Exercise 1: Find 20 consecutive composite numbers. Exercise 2: Prove that for any positive integers m and n the following relation holds: mn = gcd(m,n) . lcm(m,n). Exercise 3: Prove that there are infinitely many primes. Exercise 4: Let a and b be two relatively prime (coprime) numbers. Prove that if c is an integer such that a|c and b|c then ab|c. Exercise 5: Prove that for positive integers m and n, there exists integers x and y suchthat mx + ny = gcd(m,n).