Recent content by Pythagorean12

Homework Statement Write down the negations of the following assertions (where m, n, a, b are natural numbers): a) if Coke is not worse than Pepsi then nothing Mandelson says can be trusted. b) \forall m \exists n\forall a\forall b (n >= m) /\ [(a=1) \/ (b=1) \/ (ab \ne n)] Answers: a) if...

So, the convergents to this fraction are 1,3,3,4?

Homework Statement Find the convergents to the fraction 57/44. Homework Equations Could anyone provide any good internet resuorces about "finding the convergents to the fraction"? The Attempt at a Solution

Let's consider 3 possible cases: 1) a = 3k. This case is impossible, since from equality 10^n + 1 = a*a*c we notice that the remainder, when LHS is divided by 3, is always 2, and the remainder, when RHS is divided by 3, is 0; 2) a = 3k + 1. Then a*a = 9k*k + 6k + 1 - the remainder, when a...

Homework Statement Prove that 10^n + 1 cannot be expressed in the form a*a*c, where n,a,c are positive integers. Homework Equations By considering the reminder of 10^n + 1 when it is devided by 3, I arrived at the conclusion that: a*a = 3z +1; c = 3v + 2 for some positive integers...