p-Adic Valuation on Rationals

Explanations 3

• Prove that vp(a+b)=min⁡{vp(a),vp(b)}v_p(a+b)=\min\{v_p(a),v_p(b)\}vp​(a+b)=min{vp​(a),vp​(b)} if vp(a)≠vp(b)v_p(a)\neq v_p(b)vp​(a)=vp​(b). What can we say about vp(a+b)v_p(a+b…

  By Kada Williams

• Prove that vp(ab)=vp(a)+vp(b)v_p(ab)=v_p(a)+v_p(b)vp​(ab)=vp​(a)+vp​(b) for positive rational a,ba,ba,b.

  By Kada Williams

• We have only defined ppp-adic valuation for positive rational numbers. What about negative rationals? How would you define vp(0)v_p(0)vp​(0)? (Keep in mind the fundamental conce…

  By Kada Williams