Waste less time on Facebook — follow Brilliant.
×

Division algorithm -Doubled ,tripled

Note by Shivamani Patil
2 years, 6 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Division Algorithm states that \(a=q_{1}b+r_{1}\) where \(\leq r_{1} < b\) so we need to have \(r=r_{1} + 2b\) to get the wanted inequality. Now substituting \(r_{1}\) in terms of \(r\); \[a=q_{1}b+r-2b\] with which we can get the value of \(q\); \[a=(q_{1}-2)b+r\] Hence, \(q=q_{1}-2\), satisfying the equation \(a=qb+r\) Marc Vince Casimiro · 2 years, 5 months ago

Log in to reply

@Marc Vince Casimiro Use \leq for \( \leq \). Nice proof. Siddhartha Srivastava · 2 years, 5 months ago

Log in to reply

@Siddhartha Srivastava Thanks! Had been trying to find that LaTeX. Marc Vince Casimiro · 2 years, 5 months ago

Log in to reply

@Marc Vince Casimiro With the new display Latex tools, you just need to find some problem / note / solution with the corresponding latex that you need :) Calvin Lin Staff · 2 years, 5 months ago

Log in to reply

qb+2b<=qb+r<qb+3b , b(q+2)<=qb+r<b(q+3) , b(q+2)<=a<b(q+3),divide by b>0, q+2<=a/b<q+3, This means that rational number a/b is between two integers... Nikola Djuric · 2 years, 5 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...