MATH10040 Chapter 2: Prime and relatively prime numbers
... Again, we can see – after a bit of thought – that this can’t happen: Suppose we had equality. Divide both sides by 75 . Since 7 still divides the left-handside, it must also divide 322 · 1122 . This implies (by Corollary 2.9 again) that 7|3 or 7|11, a contradiction. ...
... Again, we can see – after a bit of thought – that this can’t happen: Suppose we had equality. Divide both sides by 75 . Since 7 still divides the left-handside, it must also divide 322 · 1122 . This implies (by Corollary 2.9 again) that 7|3 or 7|11, a contradiction. ...
number_theory_handout_II
... 1. Calculate: τ (500), σ(500), ϕ(500). 2. Calculate: τ (280), σ(280), ϕ(280). 3. How many even positive divisors does 1000 have? What is their sum? 4. What is the product of all positive divisors of 500? 5. If n = pk11 . . . pkmm is the prime factorization of n, find a formula for the product of all ...
... 1. Calculate: τ (500), σ(500), ϕ(500). 2. Calculate: τ (280), σ(280), ϕ(280). 3. How many even positive divisors does 1000 have? What is their sum? 4. What is the product of all positive divisors of 500? 5. If n = pk11 . . . pkmm is the prime factorization of n, find a formula for the product of all ...