Recent content by Colleen G

Homework Statement I need to find a bijection between (0,1) and [0,1) in R. It can go in either direction since it is a bijection. Homework Equations I can't think of any equations at all! The Attempt at a Solution Something like f(x) = 1/[(1/x)+1] for x in A...

Homework Statement If ≡(mod), ≡(mod),and gcd(,)=1,provethat ≡ (mod ). Homework Equations If ≡(mod)→n|ab-cd ≡(mod)→n|b-d gcd(,)=1→ relatively prime. So bx+ny=1 Need to show n|a-c→a-c=nw The Attempt at a Solution If n|ab-cd, then nk=ab-cd If n|b-d, then nl=b-d If n|ab-cd AND n|b-d, then...

Homework Statement If a≡b(mod n) and d=gcd(a.n), prove that d=gcd(b,n).[/B]Homework Equations If a≡b(mod n) → n|(a-b) → a-b =nk, for some k∈ℤ → a=nk+b If d=gcd(a.n) → d=ax+ny gcd(b,n)=d ↔ d|b and d|n, and if c|b and c|n, then c ≤ a. The Attempt at a Solution Since a=nk+b and d=ax+ny, then...

Thank you for you help, Dick! I understand now.

Ok yes I see that, but am having trouble using it. Are the steps that I have taken so far correct? Or have I done more than necessary. What I'm saying is, can I use this information about 3^4 from the step that I left off at?

Homework Statement Let P(n): 7|(34n+1-52n-1. Prove that P(n) is true for every natural number n. Homework Equations *I know that proving by induction requires a proving P(1) true, and then proving P(k+1) true. *If a|b, then b=a*n, for some n∈ℤ The Attempt at a Solution I have proved the "base...